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Evaluation_Word_Problems/125959: A red sports car leaves Madison traveling to Green Bay at 60 mi/hr. At the same time, a green minivan leaves Columbus traveling 40 mi/hour. Columbus is 30 miles closers to Green Bay than Madison. When will the sports car catch the minivan and at what distance from Madison? 1 solutions Answer 92326 by ankor@dixie-net.com(15653)   on 2008-02-10 13:22:58 (Show Source): You can put this solution on YOUR website! car leaves Madison traveling to Green Bay at 60 mi/hr. At the same time, a green minivan leaves Columbus traveling 40 mi/hour. Columbus is 30 miles closers to Green Bay than Madison. When will the sports car catch the minivan and at what distance from Madison? : Find the distance from Madison first : Let d = distance from Madison then (d-30) = distance from Columbus : Since they left at the same time we know their travel times will be equal : Write a time equation: Time = : = : Cross mutiply: 60(d-30) = 40d : 60d - 1800 - 40d : 60d - 40a = 1800 : 20d = 1800 d = d = 90 mi is the distance from Madison when the car catches the van : Find the time: Time = time = 1.5 hrs : : Check solution using the van's speed which travels 90 - 30 = 60 mi time = 60/40 time = 1.5 hrs also

Age_Word_Problems/125965: Ms K is 6 years more than 3 times as old as her daughter. 8 years ago she was 2 years less than 9 times as old as her daughter was then. What are thier ages? 1 solutions Answer 92313 by ankor@dixie-net.com(15653)   on 2008-02-10 11:54:17 (Show Source): You can put this solution on YOUR website! Let k = K's age now; let d = daughter's age now : Just write an equation for what it says: : "Ms K is 6 years more than 3 times as old as her daughter." k = 3d + 6 : 8 years ago they would have been (k-8) and (d-8) : "8 years ago she was 2 years less than 9 times as old as her daughter was then." (k-8) = 9(d-8) - 2 : k - 8 = 9d - 72 - 2 : k = 9d - 74 + 8 : k = 9d - 66 : What are their ages? : Substitute (3d+6) for k in the above equation, find d (3d+6) = 9d - 66 : 3d - 9d = -66 - 6 : -6d = -72 d = d = +12 yrs is the daughter's age now : Mama would be: 36 + 6 = 42 yrs old now : : Check our solutions in the statement: 8 years ago she was 2 years less than 9 times as old as her daughter was then. (42-8) = 9(12-8) - 2 34 = 9(4) - 2; confirms out solutions : Could you follow this OK? Any questions?

Percentage-and-ratio-word-problems/125956: How many ounces of a 50% acetic acid solution should a photgrapher add to 32 ounces of a 5% acetic acid solution to obtain a 10% acetic acid solution? Please help i do not know where to start with this problem. 1 solutions Answer 92310 by ankor@dixie-net.com(15653)   on 2008-02-10 11:34:00 (Show Source): You can put this solution on YOUR website! How many ounces of a 50% acetic acid solution should a photographer add to 32 ounces of a 5% acetic acid solution to obtain a 10% acetic acid solution? : Let x = amt of acetic acid required : Since this is to be added to 32 oz, the final amt will be (x+32) : Write a decimal equation: .50x + .05(32) = .10(x+32) : .5x + 1.6 = .1x + 3.2 : .5x - .1x = 3.2 - 1.6 : .4x = 1.6 x = x = 4 oz of 50% acetic acid required : : Check solution in original equation: .5(4) + .05(32) = .10(4+32) 2 + 1.6 = .1(36) 3.6 = 3.6; confirms our solution : Could you follow this OK? Did it make sense to you? Any questions?

Polynomials-and-rational-expressions/125926: Hi can you help me with this problem? The problem is a^2-2a / 4-2a.I need to simplify this rational expression. I think the answer is a/2 (a over 2). Can you show me the steps please. I want to know if I am doing it right.This question is not in my text book,it is a handout. Thanks so much! 1 solutions Answer 92303 by ankor@dixie-net.com(15653)   on 2008-02-10 10:48:57 (Show Source): You can put this solution on YOUR website! : Factor out a in the numerator and 2 in the denominator : In the denominator, change the sign outside the brackets to change the signs inside the brackets = ; : Now we can cancel out the (a-2)'s = : note that it is negative : : Did this help you? Any questions?

Quadratic_Equations/125617: how do you find the quadratic egaution of a quardratic parbolia? if the parbolia is grapghed for you and they just ask for the eguation.? 1 solutions Answer 92282 by ankor@dixie-net.com(15653)   on 2008-02-09 21:46:15 (Show Source): You can put this solution on YOUR website! how do you find the quadratic equation of a quadratic parabola? if the parabola is graphed for you and they just ask for the equation.? : Look at the x intercepts, this is the point which the graph crosses the horizontal axis : Look at this graph: : multiply the two factors from this: (x+2)(x-5) = x^2 - 3x - 10 : The fact that the intercepts multiplied together = -10, (the y intercept) tells us the coefficient of x^2 is 1

Quadratic_Equations/125815: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance, and therefore the cost of food for each member increased by $5. How many students attended the get-together? 1 solutions Answer 92276 by ankor@dixie-net.com(15653)   on 2008-02-09 21:00:16 (Show Source): You can put this solution on YOUR website! Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance, and therefore the cost of food for each member increased by $5. How many students attended the get-together? : Let x = no. of students that attended then (x+5) = no. of students anticipated to attend : The original cost per student for food: Actual cost per student: : The equation Actual cost - original cost = $5 - = 5 : Multiply each term by x(x+5) to get rid of the denominators. cancel them & you have: 500(x+5) - 500x = 5*x(x+5) : 500x + 2500 - 500x = 5x^2 + 25x : 5x^2 + 25x - 2500 = 0; 500x's cancel, arrange as a quadratic equation : Simplify divide eq by 5: x^2 + 5x - 500 = 0 : Factors to: (x + 25) (x - 20) = 0 : Positive solution is what we want: x = +20 students actually attended ; : Check solution by finding the cost per student original 500/25 = 20 actual: 500/20 = 25 --------------------- difference cost = 5

Expressions-with-variables/125662: Write the following as an algebraic expression then simplify a) The sum of three consecutive integers if x is the first consectutive integers. b)The perimeter of a square with side length 3x +1. 1 solutions Answer 92265 by ankor@dixie-net.com(15653)   on 2008-02-09 19:44:46 (Show Source): You can put this solution on YOUR website! Write the following as an algebraic expression then simplify : a) The sum of three consecutive integers if x is the first consecutive integers. Sum = x + (x+1) + (x+2) Sum = 3x + 3 Sum = 3(x+1) : b)The perimeter of a square with side length 3x +1. P = 4(3x + 1)

Travel_Word_Problems/125596: an air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff it encounters a head wind of 30 mi/hr and the wind remains constant, how far can the plane fly and then return safely. 1 solutions Answer 92262 by ankor@dixie-net.com(15653)   on 2008-02-09 19:38:48 (Show Source): You can put this solution on YOUR website! an air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff it encounters a head wind of 30 mi/hr and the wind remains constant, how far can the plane fly and then return safely. : The outbound speed: 300 - 30 = 270 mph The return speed: 300 + 30 = 330 mph : Let d = distance to the point of no return : Write a time equation: Time = : Outbound time + return time = 5 hrs + = 5 : Multiply equation by a multiple of 270 and 330, 89100 will do it: 330d + 270d = 5(89100) : 600d = 445500 d = d = 742.5 miles max distance : However, they use the word "safely", I doubt they would exceed 700 mi from home

Mixture_Word_Problems/125553: This problem is not in a book it is a hand out. If the mixture is P% gasoline, prices at $1.60 per gallon, and (100-P)% alcohol, priced at $1.00 per gallon, write a formula for the price of a gallon of gasahol. 1 solutions Answer 92226 by ankor@dixie-net.com(15653)   on 2008-02-09 16:42:24 (Show Source): You can put this solution on YOUR website! This problem is not in a book it is a hand out. If the mixture is P% gasoline, prices at $1.60 per gallon, and (100-P)% alcohol, priced at $1.00 per gallon, write a formula for the price of a gallon of gasahol. : p = per cent gasoline : f(p) = price of a gallon of gasahol. : f(p) = + ; is the gasahol formula : : We can test our formula using 50% gasoline, it should be $1.30 : f(50) = + f(50) = + f(50) = .80 + .50 f(50) = $1.30

Quadratic_Equations/125554: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer. 1 solutions Answer 92214 by ankor@dixie-net.com(15653)   on 2008-02-09 15:37:43 (Show Source): You can put this solution on YOUR website! A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer. : Looking at the first statement: "A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of row and columns, found that 24 characters were left out." : If x = number of characters in each row we translate this statement as (x*x) + 24 or x^2 + 24 = total number of characters : "When he tried to add one more row and column, he found that he was short of 25 characters." : Now, the number of rows is "x + 1", and the number of columns is "x + 1", so we have (x + 1)(x + 1) - 25 = total number of characters. : FOIL above and make it equal to the 1st equation: : x^2 + 2x + 1 - 25 = x^2 + 24 : x^2 + 2x - 24 = x^2 + 24 : x^2 - x^2 + 2x - 24 - 24 = 0 : 2x - 48 = 0 : 2x = +48 : x = 48/2 : x = 24 : : Grid is 24 by 24 which contains 576 character + 24 left out = 600 : Grid of 25 by 25 = 625 character so he would have 25 blanks : Did this make sense? Hope so.

Polynomials-and-rational-expressions/125759: Can you PLEASE help me out with a few problems? I can not figure them out to save my life. Thank you in advance!! Solve. 1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3 Solve. 2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared +2x 1 solutions Answer 92202 by ankor@dixie-net.com(15653)   on 2008-02-09 13:54:54 (Show Source): You can put this solution on YOUR website! 1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3 * : * ; canceled 5x into 10x : (x-3) * ; canceled out x : ; canceled out (x-3) : : Solve. 2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x - = : - = : Multiply equation by x(x+2) x(x+2)* - x(x+2)* = x(x+2)* Cancel out the denominators and you have: : 5(x+2) - x(x-3) = 22 : 5x + 10 - x^2 + 3x = 22; multiplied what's inside the brackets : 5x + 3x - x^2 + 10 - 22 = 0 : -x^2 + 8x - 12 = 0 : This is easier to factor if we change the signs, multiiply by -1 x^2 - 8x + 12 = 0 factors to: (x-6)(x-2) = 0 x = +6 x = +2 : : You can check both solutions in the original equation to confirm they are correct.

Rate-of-work-word-problems/125606: a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans? 1 solutions Answer 92193 by ankor@dixie-net.com(15653)   on 2008-02-09 12:53:34 (Show Source): You can put this solution on YOUR website! a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans? : Let x = time for the new machine to do the job by itself then 3x = time required for the old machine to do the job by itself, (take 3 times as long) : Let the completed job = 1; (the making of 10,000 cans) : + = 1 : Multiply equation to get rid of the denominators and you have: 9 + 3(9) = 3x : 9 + 27 = 3x : 36 = 3x x = x = 12 hrs, new machine working by itself : Check solution in original equation (old machine time 3*12 = 36hrs) + = 1 + = 1

Polynomials-and-rational-expressions/125808: This question is from textbook Introductory Algebra If anyone could help me with this problem, it would be greatly appreciated. The problem reads: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficient is -4. Find the polynomial. 1 solutions Answer 92191 by ankor@dixie-net.com(15653)   on 2008-02-09 12:27:36 (Show Source): You can put this solution on YOUR website! The problem reads: "A polynomial in x has degree 3." Write it: ax^3 + bx^2 + cx + d : The coefficient of x^2 is 3 less than the coefficient of x^3. b = a - 3 : The coefficient of x is three times the coefficient of x^2. c = 3b also, substituting (a-3) for b c = 3(a-3) c = 3a - 9 : The remaining coefficient is 2 more than the coefficient of x^3. d = a + 2 : The sum of the coefficient is -4. a + b + c + d =-4 : Using the 1st 3 equations, substitute for b, c, d: a + (a-3) + (3a-9) + (a+2) = -4 a + a - 3 + 3a - 9 + a + 2 = -4 we gather together: a + a + 3a + a - 3 - 9 + 2 = - 4 6a - 10 = -4 6a = -4 + 10 6a = 6 a = 1 Then using the 1st 3 equations, substituting 1 for a b = 1 - 3 b = -2 and c = 3(1) - 9 c = -6 and d = 1 + 2 d = 3 : Find the polynomial. : y = x^2 - 2x^2 - 6x + 3

Mixture_Word_Problems/125803: Kevin is three times as old as Bob. Three years ago the sum of their ages was 22yr. How old is each now? 1 solutions Answer 92184 by ankor@dixie-net.com(15653)   on 2008-02-09 11:15:41 (Show Source): You can put this solution on YOUR website! Write an equation for each statement: : "Kevin is three times as old as Bob." k = 3b : Three years ago, their ages; (k-3) and (b-3), right? : "Three years ago the sum of their ages was 22yr." (k-3) + (b-3) = 22 : k - 3 + b - 3 = 22 : k + b - 6 = 22 : k + b = 22 + 6 : k + b = 28 : How old is each now? : Substitute 3b for k, find b 3b + b = 28 : 4b = 28 b = b = 7 yrs old is Bob then 3(7) = 21 yrs old is Kevin : : Check our solution using the statement: "Three years ago the sum of their ages was 22yr. " (21-3) + (7-3) = 18 + 4 = 22; confirms our solution : Not that hard, do you think?

Mixture_Word_Problems/125802: Two cars start from towns 400 mi apart and travel toward each other. They meet after 4 hrs. Find the speed of each car if one travels 20mph faster than the other. 1 solutions Answer 92183 by ankor@dixie-net.com(15653)   on 2008-02-09 11:06:15 (Show Source): You can put this solution on YOUR website! Two cars start from towns 400 mi apart and travel toward each other. They meet after 4 hrs. Find the speed of each car if one travels 20mph faster than the other. : Let s = speed of the slower car then (s+20) = speed of the faster : When they meet, we know they will have traveled a total of 400 mi. : Make a distance equation: Distance = time * speed : Slow car dist + fast car dist = 400 miles 4s + 4(s+20) = 400 : 4s + 4s + 80 = 400 : 8x = 400 - 80 s = s = 40 mph is the slow car and 60 mph is the fast car : : We can check our solution by finding the total distance: 4(40) + 4(60) = 400

logarithm/125792: I don't know how to type something for exponent don't know how to type it because i have some things like 10 exponent 1-2lg10 (note 1-2lg10 is the exponent) 1 solutions Answer 92182 by ankor@dixie-net.com(15653)   on 2008-02-09 10:57:07 (Show Source): You can put this solution on YOUR website! 10 exponent 1-2lg10 (note 1-2lg10 is the exponent) : Assume you mean: : We know log of 10 is 1 : : =

Mixture_Word_Problems/125804: A table is three times as long as it is wide. If it were 3 ft shorter and 3 ft wider, it would be square (with all sides equal). How long and how wide is the table? 1 solutions Answer 92180 by ankor@dixie-net.com(15653)   on 2008-02-09 10:47:07 (Show Source): You can put this solution on YOUR website! A table is three times as long as it is wide. If it were 3 ft shorter and 3 ft wider, it would be square (with all sides equal). How long and how wide is the table? : Let x = original width then 3x = original length : If length is increased by 3 and the width is decreased by 3,it is square, therefore: (3x - 3) = (x + 3) 3x -x = 3 + 3 2x = 6 x = 3 is the width, therefore length: 3*3 = 9

Equations/125307: This question is from textbook algebra: structure and method: book1 Ingrid can rake our lawn in 90 min ad I can do it in 60 min. If she rakes for 15 min before I join her, how long will it take us to finish? PLEASE HELP!!! The answer is 30 min, but I don't know how to get there. HELP IS MUCH APPRICIATED!!!!!!!!! 1 solutions Answer 92179 by ankor@dixie-net.com(15653)   on 2008-02-09 10:12:31 (Show Source): You can put this solution on YOUR website! Ingrid can rake our lawn in 90 min and I can do it in 60 min. If she rakes for 15 min before I join her, how long will it take us to finish? : Let x = time (in min) for you to finish the job : Let the completed job = 1 : + + = 1 : Multiply equation by 180 to get rid of the denominators: 180* + 180* + 180* = 180(1) Cancel the denominators and you have: : 2(15) + 2x + 3x = 180 : 30 + 2x + 3x = 180 : 2x + 3x = 180 - 30 : 5x = 150 x = x = 30 min

Linear_Equations_And_Systems_Word_Problems/125540: The measure of the supplement of an angle is 4 times the measure of its complement. Find the measure of the angle. 1 solutions Answer 92148 by ankor@dixie-net.com(15653)   on 2008-02-08 21:43:24 (Show Source): You can put this solution on YOUR website! : Let x = the angle : The supplement: (180-x) The complement: (90-x) : write what it says: "The measure of the supplement of an angle is 4 times the measure of its complement." (180-x) = 4(90-x) : 180 - x = 360 - 4x : -x +4x = 360 - 180 : 3x = 180 x = x = 60 is the angle : : Check solution in the original equation: (180-60) = 4(90-60) 120 = 4(30); confirms our solution

Travel_Word_Problems/125513: a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream? 1 solutions Answer 92141 by ankor@dixie-net.com(15653)   on 2008-02-08 21:20:15 (Show Source): You can put this solution on YOUR website! a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream? : Let x = speed of the boat in still water Let y = speed of the current: then (x-y) = speed upstream (x+y) = speed downstream : Write a time equation for the 1st trip: time = : Time upstream + time down stream = 10 hrs + = 10 : Do the same for the second trip: + = 13 : We can use elimination; multiply the 1st eq by 4, and the 2nd eq by 3: + = 40 + = 39 ---------------------------subtraction eliminates leaving us with = 1 which is: x + y = 11 : We can replace(x+y) with 11 in the 1st trip equation + = 10 + 4 = 10 = 10 - 4 = 6 Cross multiply 6(x-y) = 30 x - y = 5; divided equation by 6 : Using these two simple equation eliminate y x + y = 11 x - y = 5 -------------adding eliminates y 2x = 16 x = 8 mph is the boat in still water then 8 + y = 11 y = 3 mph is the current : : Check our solution in the 2nd trip equation: + = 13 : : Seems like there should be a simpler way, but I can't seem to come up with tonight.

Percentage-and-ratio-word-problems/125456: Can someone please help me with this problem? If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth? My answer options are: a.33.8 yrs b.3.73 yrs c.32.8 yrs d.17.5 yrs Please get back to me as soon as possible, I am homeschooled but on a deadline to get this finished, thanks!!!! 1 solutions Answer 92127 by ankor@dixie-net.com(15653)   on 2008-02-08 19:31:42 (Show Source): You can put this solution on YOUR website! If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth? : Let t = no. of years for this to occur : We know the population in 1 yr, we can multiply 350,000 by 1.0325, therefore, the equation will be: : 350000*(1.0325)^t = 1000000 : Divide both sides by 350000 1.0325^t = 1.0325^t = 2.857 : Use the nat log of both sides: ln(1.0325^t) = ln(2.857) : The log equivalent of exponents: t * ln(1.0325) = ln(2.857) : Find the nat log of both sides: .03198t = 1.04977 t = t = 32.8258 ~ 32.8 : : Check solution on a good calc; enter 350000 * l.0325^32.8 = 999222 ~ 1000000 : You can try the other solutions and see which one is closest to 1,000,000 ~

Linear_Equations_And_Systems_Word_Problems/125537: Kelly has a purse full of quarters and dimes. There are 58 more quaters than dimes and the total value of the change is $19.05. How many dimes are there? 1 solutions Answer 92032 by ankor@dixie-net.com(15653)   on 2008-02-07 21:51:55 (Show Source): You can put this solution on YOUR website! Kelly has a purse full of quarters and dimes. There are 58 more quaters than dimes and the total value of the change is $19.05. How many dimes are there? : Let x = no. of dimes then (x+58) = no. of quarters : .10x + .25(x+58) = 19.05 : .10x + .25x + 14.5 = 19.05 : .35x = 19.05 - 14.5 : .35x = 4.55 x = x = 13 dimes : : Find the number of quarters and check the solution: 13 + 58 = 71 quarters .10(13) + .25(71) = 1.30 + 17.75 = 19.05

Linear_Equations_And_Systems_Word_Problems/125530: i need help with this problem ASAP please help me by tonight. thanks the problem says Geometry: the perimeter of a triangle is 24inches. the longest side is 4inches longer than the shortest side, and the shortest side is three fourths the length of the middle side. find the length of each side of the triangle. please help, thanks 1 solutions Answer 92030 by ankor@dixie-net.com(15653)   on 2008-02-07 21:44:29 (Show Source): You can put this solution on YOUR website! Geometry: the perimeter of a triangle is 24inches. the longest side is 4inches longer than the shortest side, and the shortest side is three fourths the length of the middle side. find the length of each side of the triangle. : Let x = length of the middle side: : Write an expression for the other two sides as described below: : "the shortest side is three fourths the length of the middle side." Short side = .75x : "the longest side is 4inches longer than the shortest side," Long side = .75x + 4 : So we have the perimeter equation: 1x + .75x + (.75x+4) = 24 : 1x + .75x + .75x + 4 = 24 : 2.5x = 24 - 4; add up the x's, subtract 4 from both sides : 2.5x = 20 x = ; divide both sides by 2.5 x = 8 inches is the length of the middle side Then .75(8) = 6 inches is the length of short side and 6 + 4 = 10 inches is the length of the long side ; : Check our solution, find the perimeter with these values: 8 + 6 + 10 = 24 inche : : How about this? Did this all make sense to you. Any questions?

Circles/125418: I need help solving the rest of this math question. May answer for the circumference is 62.83 ft, but I didn't know how to calculate the area. What is the circumference and area in feet of circular pool that has a diameter of 20 yards? 1 solutions Answer 92027 by ankor@dixie-net.com(15653)   on 2008-02-07 21:29:58 (Show Source): You can put this solution on YOUR website! What is the circumference and area in feet of circular pool that has a diameter of 20 yards? : You should be familiar with the "Area of a circle equation: A = pi*r^2 : If the diameter is 20, the radius is 10, : A = pi*10^2 A = pi*100 A = 314.16 sq/ft

Travel_Word_Problems/125417: I just need to figure out the formula to solve this problem. On the first part of a 317-mile trip, a salesperson averaged 58 miles per hour. He averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds?????? 1 solutions Answer 92023 by ankor@dixie-net.com(15653)   on 2008-02-07 21:18:00 (Show Source): You can put this solution on YOUR website! On the first part of a 317-mile trip, a salesperson averaged 58 miles per hour. He averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds. : Change 5 hr 45 min to hrs: 5.75 hrs : Let t = time spent at 58 mph : It said the total time was 5.75 hrs, therefore: (5.75 - t) = time spent at 52 mph : Write a distance equation: Distance = speed * time : 58mph dist + 52mph dist = 317 miles : 58t + 52(5.75-t) = 317 Here is the equation, you can take it from there. :

Travel_Word_Problems/125594: a park has two sprinklers that are used to fill a fountain. one sprinkler can fill the fountain in 3 hrs, wheras the secound sprinkler can fill the fountain in 6 hours. how long will it take to fill the fountain using both sprinklers. 1 solutions Answer 92014 by ankor@dixie-net.com(15653)   on 2008-02-07 20:32:46 (Show Source): You can put this solution on YOUR website! a park has two sprinklers that are used to fill a fountain. one sprinkler can fill the fountain in 3 hrs, whereas the second sprinkler can fill the fountain in 6 hours. how long will it take to fill the fountain using both sprinklers. : Let t = time required with both sprinklers working : Let the completed job = 1 : + = 1 Multiply equation by 6 6* + 6* = 6(1) : Cancel out the denominators and you have: 2t + t = 6 : 3t = 6 t = t = 2 hrs working together : We can confirm this by t=2 in the original equation: + = 1

Quadratic_Equations/125441: What would the graph of the quadratic function with zeros 1/2 plus or minus sqrt7/3 look like ? 1 solutions Answer 92012 by ankor@dixie-net.com(15653)   on 2008-02-07 20:26:17 (Show Source): You can put this solution on YOUR website! What would the graph of the quadratic function with zeros 1/2 plus or minus sqrt7/3 look like ? : In order to graph it, you need the equation, find that: x = : x - = +/-; subtract from both sides : (x-)^2 = ; squared both sides : x^2 - 1x + = ; FOILed : x^2 - 1x + - = 0; Subtracted from both sides : x^2 - 1x + - = 0; use a common denominator : x^2 - 1x - = 0 : Plot this equation from x = -2 to x = +3, it should look like this: : Could you follow this OK?

Graphs/125401: Theater tickets are $8 for general admission (GA) and $5 for students (STD). During one evening 240 tickets were sold, and the receipts were $1680. How many of each type of ticket was sold? HELP!!!!!! 1 solutions Answer 92007 by ankor@dixie-net.com(15653)   on 2008-02-07 20:01:56 (Show Source): You can put this solution on YOUR website! Theater tickets are $8 for general admission (GA) and $5 for students (STD). During one evening 240 tickets were sold, and the receipts were $1680. How many of each type of ticket was sold? : Let x = no. of GA tickets Let y = no. of STD tickets : Translate these two statements to equations: : During one evening 240 tickets were sold," x + y = 240 or y = (240 - x); we can use this for substituting below : "tickets are $8 for general admission (GA) and $5 for students (STD).... the receipts were $1680." 8x + 5y = 1680 : How many of each type of ticket was sold? ; Substitute (240-x) for y in the above equation, find x: 8x + 5(240-x) = 1680 : 8x + 1200 - 5x = 1680; multiplied what's inside the brackets : 8x - 5x = 1680 - 1200 : 3x = 480 x = x = 160 Ga tickets : Find y: y = 240 - x y = 240 - 160 y = 80 STD tickets : : Check solution in the receipt$ equation 8(160) + 5(80) = 1280 + 400 = 1680 : Did I make this understandable? Think you can do these type of equations now?

Linear_Equations_And_Systems_Word_Problems/125444: How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get 20% mixture? 1 solutions Answer 91999 by ankor@dixie-net.com(15653)   on 2008-02-07 19:44:39 (Show Source): You can put this solution on YOUR website! How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get 20% mixture? : Let x = amt of pure acid required : This is to be mixed with 20 liters, therefore: The amt of the final mixture will = (x+20) : Pure acid will be 1.0x : .15(20) + 1.0x = .20(x+ 20) : 3 + 1x + .20x + 4 : 1x - .2x = 4 - 3 : .8x = 1 x = x = 1.25 liters of pure acid to produce a 20% mixture : : Check .15(20) + 1.25 = .20(21.25) 3 + 1.25 = 4.25; confirms our solution

Travel_Word_Problems/125584: a long distance runner, runs at an average velocity of 8mph. Two hours after Tanya leaves your house, you leave in your honda and follow the same route. If your average velocity is 40 mph, how long will it be before you catch up with Tanya? How far will you be from your home? 1 solutions Answer 91995 by ankor@dixie-net.com(15653)   on 2008-02-07 19:32:57 (Show Source): You can put this solution on YOUR website! a long distance runner, runs at an average velocity of 8mph. Two hours after Tanya leaves your house, you leave in your honda and follow the same route. If your average velocity is 40 mph, how long will it be before you catch up with Tanya? How far will you be from your home? : Let t = time required for you to catch up with T Then (t+2) = T's travel time when she is caught : One thing to remember in any of these "catch-up programs" is both of you travel the same distance, write a simple distance equation from this fact. : Distance = speed * time : Your dist = T's distance 40t = 8(t+2) : 40t = 8t + 16 : 40t - 8t = 16 : 32t = 16 t = t = hr for you to catch up : Find the distance using t = .5 hr for you and 2.5 hr for T 40 * .5 = 20 mi 8 * 2.5 = 20 mi also; confirms our solution

Inverses/125574: This question is from textbook Mathematics 10 1/2(x-5)=x/4 I have tried this question so many ways, my head hurts. I can't figure it out! I only need one example and I will be able to complete my homework, unfortunately the text book does not give me an example. I have plans to go into school early if you can't help, but I thought I would give this a shot. I like to work things out on my own, but this is review from last year and after not seeing math problems for a year I'm struggling. Thanks 1 solutions Answer 91991 by ankor@dixie-net.com(15653)   on 2008-02-07 19:22:53 (Show Source): You can put this solution on YOUR website! (x-5) = : The first thing you want to do here is get rid of the denominators multiply equation by a multiple of both denominators, that would 4 4*(x-5) = 4* Cancel out the denominators and you have: 2(x-5) = 1x : 2x - 10 = x; multiply what's inside the brackets : 2x - x = +10; basic algebra, add 10 to both sides, subtract x from both side : x = 10 : : Check in original equation; substitute 10 for x (10-5) = (5) = 2.5 = 2.5