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 Travel_Word_Problems/638504: Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs. In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home?1 solutions Answer 402407 by ankor@dixie-net.com(15661)   on 2012-08-19 16:04:17 (Show Source): You can put this solution on YOUR website! Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs.Le In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home? : Let s = the walking speed and 2s = the running speed : From the information given, we know she walked (20)min and ran (20)min Using decimals, walked 13.33 min and ran 6.67 min Find the distance; dist = time * speed 13.33s + 6.67(2s) = 26.67s is the distance one way : "On her way home, she runs for twice the length of time as she walks." let t = time she walked going home then 2t = time she ran going home Another distance equation st + 2s(2t) = 26.67s st + 4st = 26.67s Divide thru by s t + 4t = 26.67 5t = 26.67 t = t = 5 spent walking and 10 spend running then total time to return 5 + 10 = 16 min to return home
 Miscellaneous_Word_Problems/638374: A wire of length 16 inches is to be cut into two pieces; then each piece will be bent to form a square. Find the length of the two pieces assuming that the sum of the areas of the two squares is 10 square inches.1 solutions Answer 402279 by ankor@dixie-net.com(15661)   on 2012-08-18 17:16:18 (Show Source): You can put this solution on YOUR website!A wire of length 16 inches is to be cut into two pieces; then each piece will be bent to form a square. Find the length of the two pieces assuming that the sum of the areas of the two squares is 10 square inches. : Let the length of the sides of the two square be x & y : 4x + 4y = 16 simplify, divide by 4 x + y = 4 y = (4-x) and x^2 + y^2 = 10 : Replace y with (4-x) x^2 + (4-x)^2 = 10 FOIL (4-x)(4-x) x^2 + 16 - 8x + x^2 = 10 Combine like terms on the left x^2 + x^2 - 8x + 16 - 10 = 0 2x^2 - 8x + 6 = 0 simplify, divide by 2 x^2 - 4x + 3 = 0 Factors to (x-1)(x-3) = 0 Two solutions x = 1, then y = 3 and x = 3, then y = 1 : : You can check if this is true in the two original equations
 Travel_Word_Problems/638031: The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers?1 solutions Answer 402276 by ankor@dixie-net.com(15661)   on 2012-08-18 16:56:50 (Show Source): You can put this solution on YOUR website!The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers? : Let s = speed of the two hikers then (s+1) = speed of the A after his 1 hr rest : Find the distance hiker A traveled after his rest, to meet B, 4 km from City B 28-9-4 = 15 km : Write a time equation; time = dist/speed + + 1 = : + = - 1 : = : = : = Multiply both sides by s = (4 - s) 24s + 9 = (s+1)(4-s) FOIL the right side 24s + 9 = 4s - s^2 + 4 - s 24s + 9 = 3s - s^2 + 4 Combine on the left s^2 + 24s - 3s + 9 - 4 = 0 s^2 + 21s + 5 = 0 Actually this equation has two negative solutions so the given scenario is not possible. It seems unreasonable, to find a speed, where A travels 24 km (+ a rest), while B travels 4 km
 Travel_Word_Problems/638020: At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance of the trail?1 solutions Answer 402254 by ankor@dixie-net.com(15661)   on 2012-08-18 13:25:18 (Show Source): You can put this solution on YOUR website!At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance : Do this using minutes for the time let t = travel time to the point where they met : let x = dist from A to the meeting point and (x+2) = dist from B to the meeting point then x + (x+2) = 2x+2 km is the distance from A to B : A<-----40min------*---------t min-------< B(hiker B's path) A------x km-------*-------(x+2)km-------B A>-----t Min------*--------90min--------> B (hiker A's path) : Hiker B, = Cross multiply tx = 40(x+2) tx = 40x + 80 t = : Hiker A = Cross multiply t(x+2) = 90x t = : t=t, therefore: = Cross multiply 90x^2 = (x+2)(40x+80) FOIL 90x^2 = 40x^2 + 80x + 80x + 160 90x^2 = 40x^2 + 160x + 160 Combine on the left 90x^2 - 40x^2 - 160x - 160 = 0 50x^2 - 160x - 160 = 0 Simplify, divide by 10 5x^2 - 16x - 16 = 0 Factors to (5x + 4)(x - 4) = The positive solution is all we want here x = 4 "What is the distance?" 2(4) + 2 = 10 km is the distance from A to B : : Confirm this, find t t = t = 60 min Find the speed of A & B A's time in hrs (90+60)/60 = 2.5 hrs A's speed 10/2.5 = 4 km/hr and B's time in hrs (40+60)/60 = 1 hrs A's speed 10/1.67 ~ 6 km/hr : Find how far each traveled in 1 hr (t) B: 6 km A: 4 km --------- dif: 2 km
 Linear_Equations_And_Systems_Word_Problems/638354: A professor announces that course grades will be computed by taking 40% of a student's project score (0-100 points) and adding 60% of the students final exam score (0-100 points). If a student gets an 86 on the project, what scores can she get on the final exam to get a course grade of at least 90? These are some conclusions I've made, which may or may not be correct. 40%(86)+60%(x) is greater than or equal to 90. I am confused by the word "And" in the problem. Does this let me know that this is a compound inequality? If so, what other numbers do I use to create another inequality...100? 1 solutions Answer 402160 by ankor@dixie-net.com(15661)   on 2012-08-17 18:55:42 (Show Source): You can put this solution on YOUR website! professor announces that course grades will be computed by taking 40% of a student's project score (0-100 points) and adding 60% of the students final exam score (0-100 points). If a student gets an 86 on the project, what scores can she get on the final exam to get a course grade of at least 90? : Here is one equation for this, the relationship between the project and final exam is 4:6 : x = students grade on the final exam => 90 => 90 multiply both sides by 10 344 + 6x => 900 6x => 900 - 344 x => 556/6 x => 93 on the final exam to achieve an average of 90 for the course : : You can confirm this: .4(86) + .6(93) = 90.2 (we rounded up 92.6667)
 Surface-area/638263: How long is the piece of wood needed to frame a picture which measures 25 cm by 36 cm and the width of the wood is 3 cm?1 solutions Answer 402155 by ankor@dixie-net.com(15661)   on 2012-08-17 18:11:09 (Show Source): You can put this solution on YOUR website!How long is the piece of wood needed to frame a picture which measures 25 cm by 36 cm and the width of the wood is 3 cm? : A 3 cm wide frame will add 6 cm to each dimension 31 by 42 cm will be the dimensions which include the frame : Total amt of wood will be the perimeter p = 2(31)+2(42) p = 146 cm for 3 cm wide frame
 Polynomials-and-rational-expressions/637987: solve for x: log(2x-1) = 11 solutions Answer 402152 by ankor@dixie-net.com(15661)   on 2012-08-17 18:01:46 (Show Source): You can put this solution on YOUR website!solve for x: log(2x-1) = 1 Write the exponent equiv of logs (2x-1) = 10^1 2x - 1 = 10 2x = 10 + 1 2x = 11 x = 11/2 x = 5.5 : : Check this on your calc, enter: log(2(5.5)-1)
 logarithm/637942: solve for x and round the answer to the nearest hundreth. 5 = ln(x + 1)1 solutions Answer 401979 by ankor@dixie-net.com(15661)   on 2012-08-16 14:44:07 (Show Source): You can put this solution on YOUR website!solve for x and round the answer to the nearest hundreth. 5 = ln(x + 1) ln(x+1) = 5 Find of both sides x + 1 = 148.41 x = 148.41 - 1 x = 147.41 : Check this on your calc, enter ln(147.41+1), results 4.9999 ~ 5
 Travel_Word_Problems/637688: x & y travel 4000m n finish race in tie.first x travel 50% than Y and Y travels 50% faster than x n end in tie.before y travelled 50% faster then X what distance had it covered?1 solutions Answer 401928 by ankor@dixie-net.com(15661)   on 2012-08-15 22:01:30 (Show Source): You can put this solution on YOUR website!Attempt to rewrite this so it makes sense. : x & y travel 4000m and finish the race in a tie. At first x travels 50% faster than Y and then, Y travels 50% faster than x, and the race ends in a tie. Before y traveled 50% faster then X, what distance had he covered? : let s = the original speed of y and 1.5s = the original speed of x then 1.5(1.5s)= 2.25s = final speed of y : Let d = distance y traveled at speed s then (4000-d) = speed y traveled at speed 2.25s : Write a time equation: y's total travel time = x's travel time + = Multiply by least common multiple: 27s 27s* + 27s* = 27s* Cancel out the denominators, results: 27d + 12(4000-d) = 18(4000) 27d + 48000 - 12d = 72000 27d - 12d = 72000 - 48000 15d = 24000 d = d = 1600 meters traveled before y changed his speed to 1.5 times x's speed
 Age_Word_Problems/637410: 14. The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum the ages of his children will be twice the ages of their father. Find the present age of the father.1 solutions Answer 401899 by ankor@dixie-net.com(15661)   on 2012-08-15 19:31:40 (Show Source): You can put this solution on YOUR website!The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum the ages of his children will be twice the ages of their father. Find the present age of the father. : let f = father's present age let s = sum of the 5 children's now then f = s "12 years hence, the sum the ages of his children will be twice the ages of their father." (12 yrs hence, add 12 to each of the five children) 2(f + 12) = s + 5(12) 2f + 24 = s + 60) 2f = s + 60 - 24 2f = s + 36 replace s with f 2f = f + 36 2f - f = 36 f = 36 yrs is the father's present age
 Travel_Word_Problems/637714: An ambulance left the hospital and drove south. 3 hours later a police car left driving 42 k/h faster attempting to catch up to the ambulance. The officer caught up after 2 hours. Find the average speed of the ambulance.1 solutions Answer 401869 by ankor@dixie-net.com(15661)   on 2012-08-15 16:25:55 (Show Source): You can put this solution on YOUR website!An ambulance left the hospital and drove south. 3 hours later a police car left driving 42 k/h faster attempting to catch up to the ambulance. The officer caught up after 2 hours. Find the average speed of the ambulance. : Let a = the speed of the ambulance then (a+42) = the speed of the police car : From the information given, we know the travel time of the ambulance = 5 hrs and the Cop = 2 hrs : When the cop catches the amb, they will have traveled the same distance Write a distance equation dist = speed * time : 5a = 2(a+42) 5a = 2a + 84 5a - 2a = 84 3a = 84 a = 84/3 a = 28 mph speed of the ambulance : : Confirm this by finding the distances, should be equal 5(28) = 140 km 2(28+42) = 140 km
 Mixture_Word_Problems/637707: A metallurgist needs to make 12.4 lbs. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use?1 solutions Answer 401851 by ankor@dixie-net.com(15661)   on 2012-08-15 15:15:51 (Show Source): You can put this solution on YOUR website!A metallurgist needs to make 12.4 lbs. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use? : Common sense says that it would be half 50% alloy and half 40% alloy But here is a the mixture equation : Let x = amt of 60% gold alloy required the total is to be 12.4 lbs, therefore: (12.4-x) = amt of 40% alloy required : Decimal equiv equation .60x + .40(12.4-x) = .50(12.4) .60x + 4.96 - .40x = 6.2 .60x - .40x = 6.2-4.96 .20x = 1.24 x = 1.24/.2 x = 6.2 lbs of the 60% alloy then 12.4 - 6.2 = 6.2 lbs of 40% alloy : : Check this .6(6.2) + .4(6.2) = .5(12.4) 3.72 + 2.48 = 6.2 6.2 = 6.2
 Quadratic_Equations/637693: A kicker starts a football game by "kicking off". The quadratic function y = -12⋅x2 + 36⋅x models the football's height after x seconds. How long is the football in the air?1 solutions Answer 401844 by ankor@dixie-net.com(15661)   on 2012-08-15 14:41:30 (Show Source): You can put this solution on YOUR website!A kicker starts a football game by "kicking off". The quadratic function y = -12⋅x2 + 36⋅x models the football's height after x seconds. How long is the football in the air? : y = -12x^2 + 36x When the ball hits the ground, y = 0; therefore: -12x^2 + 36x = 0 Factor out -12x -12x(x - 3) = 0 Two solutions x = 0 and x = 3 seconds in the air
 Travel_Word_Problems/637717: A car needs 1 minute 30 secondes to travel a distance of 1 mile. At this rate how many miles will the car travel in 1 hour?1 solutions Answer 401839 by ankor@dixie-net.com(15661)   on 2012-08-15 14:35:10 (Show Source): You can put this solution on YOUR website!A car needs 1 minute 30 seconds to travel a distance of 1 mile. At this rate how many miles will the car travel in 1 hour?: : Find the mph; speed = dist/time Change 1.5 min to hrs, 1.5/60 = .025 hrs : s = s = 40 mph
 Mixture_Word_Problems/637708: 9 quarts of a sugar solution was mixed 6 quarts of a 90% sugar solution to make an 84% sugar solution. What is the percent concentration of the first solution?1 solutions Answer 401836 by ankor@dixie-net.com(15661)   on 2012-08-15 14:22:37 (Show Source): You can put this solution on YOUR website!9 quarts of a sugar solution was mixed 6 quarts of a 90% sugar solution to make an 84% sugar solution. What is the percent concentration of the first solution? : Let x = the decimal equiv of the required percentage of the 1st solution The total amt: 9 + 6 = 15 qts : 9x + .90(6) = .84(15) 9x + 5.4 = 12.6 9x = 12.6-5.4 9x = 7.2 x = 7.2/9 x = .8 which is an 80% solution :
 Average/637704: 6-w=1 4/5 I know how to find the answer by using common sense. However, I'm used to problems like this: w - 6=1 4/5 I would know to use the opposite operation and add 6 to both sides, etc...I just don't know the formula on figuring out the original problem. My textbook does not give me any guidance or example problems. 1 solutions Answer 401834 by ankor@dixie-net.com(15661)   on 2012-08-15 14:11:25 (Show Source): You can put this solution on YOUR website!6-w=1 4/5 convert mixed number to an improper fraction; 5/5 + 4/5 6 - w = multiply both sides by 5 to get rid of the denominator 5(6-w) = 9 30 - 5w = 9 Subtract 9 from both sides, add 5w to both sides 30 - 9 = 5w 21 = 5w Divide both sides by 5 w = or 4 as a mixed number : : Check this out in the original problem using improper fractions 6 - = Convert 6 to an improper fraction with 5 as the denominator - =
 Rate-of-work-word-problems/637716: Answer this school maths question - If it takes three men three hours to dig a hole, how long would it take one man to dig a hole of the same size? *1 solutions Answer 401830 by ankor@dixie-net.com(15661)   on 2012-08-15 13:51:46 (Show Source): You can put this solution on YOUR website!If it takes three men three hours to dig a hole, how long would it take one man to dig a hole of the same size? : Find the number of man-hours required to dig a hole. 3*3 = 9 man-hrs let h = no. of hrs for 1 man to do it 1h = 9 h = 9 hrs
 Age_Word_Problems/637661: four times the sum of the digits of a two-digit number is equal to the number.if digits are reserved, the resulting number is 27 greater than the original number. what is the number? 1 solutions Answer 401829 by ankor@dixie-net.com(15661)   on 2012-08-15 13:47:10 (Show Source): You can put this solution on YOUR website!Let a = the 10's digit let b = the units then 10a+b = the original number : Write an equation for each statement: : "four times the sum of the digits of a two-digit number is equal to the number." 4(a+b) = 10a + b 4a + 4b = 10a + b 4b - b = 10a - 4a 3b = 6a divide both sides by 3 b = 2a : "if digits are reserved, the resulting number is 27 greater than the original number." 10b + a = 10a + b + 27 10b - b = 10a - a + 27 9b = 9a + 27 divide by 9 b = a + 3 replace b with 2a (from the 1st statement) 2a = a + 3 2a - a = 3 a = 3 you can find b, I'm sure what is the number?
 Radicals/637713: What is the best way to solve this equation in step by step ? I'm profoundly grateful for help. 1 solutions Answer 401827 by ankor@dixie-net.com(15661)   on 2012-08-15 13:21:03 (Show Source): You can put this solution on YOUR website!solve this equation in step by step ? = Square both sides = : FOIL )*( : Results - - + = : 2x/2x = 1, square root of 1 is 1 therefore - 1 - 1 + = : - 2 + = : Multiply each term by 2x, to clear the denominators, results 2(2) - 4x + x^2 = x Combine on the left to form a quadratic equation x^2 - 5x - x + 4 = 0 x^2 - 5x + 4 = 0 Factors to: (x-4)(x-1) = 0 two solutions x=4 x=1
 Linear_Equations_And_Systems_Word_Problems/637513: During the class period,the number of girls is ten more than four times the number of boys.formulate two linear equations from the statement to determine the number of boys in the class if the total number of students in that class is one hundred.let the number of boys be represented by variable y and let the number of girls be represented by variable x.1 solutions Answer 401749 by ankor@dixie-net.com(15661)   on 2012-08-14 21:02:10 (Show Source): You can put this solution on YOUR website!During the class period,the number of girls is ten more than four times the number of boys. formulate two linear equations from the statement to determine the number of boys in the class if the total number of students in that class is one hundred. let the number of boys be represented by variable y and let the number of girls be represented by variable x. : Write an equation for each statement: : "the number of girls is ten more than four times the number of boys.' x = 4y + 10 : "the total number of students in that class is one hundred." x + y = 100