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 Rate-of-work-word-problems/699386: One pipe can fill a tank in 2 hours. A second pipe can fill it in 1.75 hours. How long will it take to fill the tank with both pipes open? Thank you so much1 solutions Answer 431373 by ankor@dixie-net.com(15667)   on 2013-01-07 21:53:48 (Show Source): You can put this solution on YOUR website!One pipe can fill a tank in 2 hours. A second pipe can fill it in 1.75 hours. How long will it take to fill the tank with both pipes open? : Let t = time required when working together Let the completed job = 1; (a full tank) : Each pipe will do a fraction of the job, the two fractions add up to 1 : t/2 + t/1.75 = 1 multiply both sides by 14, resulting 7t + 8t = 14 15t = 14 t = 14/15 hrs or t = 14/15 *60 = 56 min working together
 Miscellaneous_Word_Problems/699095: if nails are bought at 35 cents per dozen and sold at 3 for 10 cents, the profit on dozen is? note dozen denotes a quantity consisting of items or units1 solutions Answer 431370 by ankor@dixie-net.com(15667)   on 2013-01-07 21:44:34 (Show Source): You can put this solution on YOUR website!if nails are bought at 35 cents per dozen and sold at 3 for 10 cents, the profit on dozen is? : Find the selling price of a dozen nails (4 sets of 3 = 12) 4 * 10 = 40 cents for 12 : 40 - 35 = 5 cents profit on a dozen nails
 Age_Word_Problems/699100: Jones is now twice as old as he was 5 years ago and his mother is now four times as old as jones.How old is his mother1 solutions Answer 431367 by ankor@dixie-net.com(15667)   on 2013-01-07 21:39:46 (Show Source): You can put this solution on YOUR website!Jones is now twice as old as he was 5 years ago j = 2(j-5) j = 2j - 10 10 = 2j - j j = 10 yrs old now : mother is now four times as old as jones m = 4j m = 4(10) m = 40 yrs is Mom's age
 Linear-equations/699383: solve the following system x+2y+1=0 xy-y=01 solutions Answer 431363 by ankor@dixie-net.com(15667)   on 2013-01-07 21:26:18 (Show Source): You can put this solution on YOUR website!x + 2y + 1 = 0 : xy - y = 0 xy = y divide both sides by y x = 1 : Replace x in the 1st equation with 1, find y 1 + 2y + 1 = 0 2y + 2 = 0 2y = -2 y = -1 : solution: x=1, y=-1
 Polynomials-and-rational-expressions/699309: We are to use zero product property on this problem: 9k to the second power=4k I did this: 9k to the second power minus 4k=0 which was what our teacher told us to do but I don't know what to do after this. Please help 1 solutions Answer 431352 by ankor@dixie-net.com(15667)   on 2013-01-07 20:18:25 (Show Source): You can put this solution on YOUR website!9k^2 = 4k 9k^2 - 4k = 0 Factor out k k(9k - 4) = 0 Two solutions k = 0 and 9k = 4 k = 4/9
 Numbers_Word_Problems/699355: A certain number is subtracted from 20. The result multiplied by 3 is equal to 45 what is the number? I can normally do word problems with no problem but since I quit going to school and now taking my GED classes I can't remember how to put the word problem into an equation to figure out the answer if you could please help me it would be greatly appreciated thanks -Jessica 1 solutions Answer 431350 by ankor@dixie-net.com(15667)   on 2013-01-07 20:10:49 (Show Source): You can put this solution on YOUR website!A certain number is subtracted from 20. The result multiplied by 3 is equal to 45 what is the number? : 3(20-n) = 45 60 - 3n = 45 -3n = 45 - 60 -3n = -15 n = -15/-3 n = +5 : Hopefully, you are returning to school, I wish you luck. C
 Geometry_Word_Problems/699066: "This is the problem. Would you please help me with this? Thank You!" ---> A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours. A became ill and B continuing the work alone finished it in 33/4 hours. How long would it take each working alone to do the job?1 solutions Answer 431291 by ankor@dixie-net.com(15667)   on 2013-01-07 16:43:36 (Show Source): You can put this solution on YOUR website!A and B working together can finish a certain job in 20/3 hours. They start the work together, but after 3 hours, A became ill and B continuing the work alone. finished it in 33/4 hours. How long would it take each working alone to do the job? : let a = A doing the job alone let b = B doing it alone : Let the completed job = 1 : Write a share work equation for the statement: "A and B working together can finish a certain job in 20/3 hours." + = 1 invert the divisor and multiply + = 1 multiply by 3ab, results 20b + 20a = 3ab : " They start the work together but after 3 hours, A became ill and B continuing the work alone, finished it in 33/4 hours. How long would it take each working alone to do the job?" : Change 33/4 hrs to 8.25 hrs B works 3 + 8.25 = 11.25 hrs + = 1 multiply by ab to clear the denominators 3b + 11.25a = ab : Try to use elimination with these two equations 3b + 11.25a = ab 20b + 20a = 3ab Multiply the 1st equation by 20, multiply the 2nd equation by 3 60b + 225a = 20ab 60b + 60a = 9ab -----------------subtraction eliminates b 165a = 11ab divide both side by a 165 = 11b b = 165/11 b = 11 hrs working alone : Find a, 20b + 20a = 3ab replace b with 11 20(11) + 20a = 3(a*11) 220 + 20a = 33a 220 = 33a - 20a 220 = 13a a = 220/13 a = 16 hrs working alone : : Check this in the 1st work statement equation but we will use decimals instead of those annoying fractions + = .394 + .606 = 1; confirms our solutions
 Problems-with-consecutive-odd-even-integers/699093: Hello! I am a bit confused with this problem. PLEASE HELP ME. find three consecutive even integers such that their sum decreased by the third is 82. 1 solutions Answer 431278 by ankor@dixie-net.com(15667)   on 2013-01-07 15:43:23 (Show Source): You can put this solution on YOUR website!find three consecutive even integers x, (x+2, (x+4) : Just write what it says," such that their sum decreased by the third is 82. x + (x+2) + (x+4) - (x+4) = 82 2x + 2 = 82 2x = 82 - 2 2x = 80 x = 40 ; Check: 40 + 42 + 44 - 44 = 82
 Travel_Word_Problems/699088: A person covers half his journey by bus at 60 km/hr, half the remaining half by train at 30 km/hr and the rest by cycle at 10 km/hr. Find the average speed ?1 solutions Answer 431206 by ankor@dixie-net.com(15667)   on 2013-01-07 10:06:25 (Show Source): You can put this solution on YOUR website!A person covers half his journey by bus at 60 km/hr, half the remaining half by train at 30 km/hr and the rest by cycle at 10 km/hr. Find the average speed ? : Let j = total length of the journey then .5j = bus length .25j = train length .25j = bike length : let s = average speed of the whole journey : Write a time equation; time = dist/speed : bus time + train time + bike time = total time + + = multiply by 60s to get rid of the denominators, results .5js + 2(.25js) + 6(.25js) = 60j .5js + .5js + 1.5js = 60j 2.5js = 60j divide both sides by j 2.5s = 60 s = 60/2.5 s = 24 km/h, average speed for the trip
 Age_Word_Problems/699133: The present age of A and his father is in the ratio of 2:5 respectively.4 years hence the ratio of their ages will become 5:11 respectively.what was father's age 5 years ago?1 solutions Answer 431193 by ankor@dixie-net.com(15667)   on 2013-01-07 08:08:39 (Show Source): You can put this solution on YOUR website!The present age of A and his father is in the ratio of 2:5 respectively. = Cross multiply 5a = 2f a = f a = .4f : 4 years hence the ratio of their ages will become 5:11 respectively. = cross multiply 11(a+4) = 5(f+4) 11a + 44 = 5f + 20 11a = 5f + 20 - 44 11a = 5f - 24 replace a with .4f 11(.4f) = 5f - 24 4.4f = 5f - 24 24 = 5f - 4.4 24 = .6f f = 24/.6 f = 40 yrs is Dad's present age then a = .4(40) a = 16 is A's present age : what was father's age 5 years ago? You can figure that out, I know
 Equations/698987: a number of 3 digits is such hat the tens digit exceeds the unit digit by 2. If this number exceeds the number formed by reversing the digits 297 ad if the sum of its digits is 14, find the number. 1 solutions Answer 431171 by ankor@dixie-net.com(15667)   on 2013-01-06 21:59:59 (Show Source): You can put this solution on YOUR website!a number of 3 digits is such hat the tens digit exceeds the unit digit by 2. If this number exceeds the number formed by reversing the digits by 297 and if the sum of its digits is 14, find the number. : Let a = the 100's digit Let b = the 10's digit Let c = the units then 100a + 10b + c = "the 3digit number and 100c + 10b + a = the number reversed : " the tens digit exceeds the unit digit by 2." b = c+2 : " If this number exceeds the number formed, by reversing the digits by 297" 100a + 10b + c = 100c + 10b + a + 297 Combine like terms 100a - a + 10b - 10b = 100c - c + 297 99a = 99c + 297 Simplify, divide by 99 a = c + 3 : "the sum of its digits is 14," a + b + c = 14 replace a with (c+3), replace b with (c+2) c + 3 + c + 2 + c = 14 3c + 5 = 14 3c = 14 - 5 c = 9/3 c = 3 : I'll let you find a and b check the number you come up with in each statement :
 logarithm/698920: How do I solve the following problem for X? Please exact or round to hundredths. 7^2x+1=3^x+21 solutions Answer 431170 by ankor@dixie-net.com(15667)   on 2013-01-06 21:42:40 (Show Source): You can put this solution on YOUR website!Assume the problem is: using logs The log equiv of exponents (2x+1)log(7) = (x+2)log(3) Find the logs of 7 and 3 .8451(2x+1) = .4771(x+2) 1.6902x + .8451 = .4771x + .9542 1.6901x - .4771x = .9542 - .8451 1.213x = .1091 x = x ~ .09 : : You can check this on your calc, replace x with .09 in the 1st equation, confirm they are equal
 Travel_Word_Problems/698932: Two cars leave an intersection. One car travels North the other travels East. When the car traveling North had gone 63 miles, the distance between the cars was 17 miles more than three times the distance traveled by the car heading East. Find the distance between the cars at that time. 1 solutions Answer 431167 by ankor@dixie-net.com(15667)   on 2013-01-06 21:29:10 (Show Source): You can put this solution on YOUR website! Two cars leave an intersection. One car travels North the other travels East. When the car traveling North had gone 63 miles, the distance between the cars was 17 miles more than three times the distance traveled by the car heading East. Find the distance between the cars at that time. : This is a Pythagoras problem a^2 + b^2 = c^2, where: a = 63, northbound car dist) b = Eastbound car dist c = distance between the cars at this time "the distance between the cars was 17 miles more than three times the distance traveled by the car heading East c = 3b + 17 : 63^2 + b^2 = (3b+17)^2 FOIL the right side 3969 + b^2 = 9b^2 + 51b + 51b + 289 Combine like terms on the right 0 = 9b^2 - b^2 + 102b + 289 - 3969 0 = 8b^2 + 102b - 3680 Simplify, divide by 2 4b^2 + 51b - 1840 = 0 Use the quadratic formula to find b the positive solution should be b = 16 then 3(16) + 17 = 65 mi is the distance between the cars at this time ; : Check this on your calc: enter results: 65
 Travel_Word_Problems/698862: if we knew that we traveled 300 miles in 5 hours and wanted to find our average rate of speed? How would I figure out what my speed was??? I know take a number lets say 50mph divided into 300miles = 6 So is the answer 60 mph correct? how would I figure out the answer to the question by only looking at 300mi in 5hrs? 1 solutions Answer 431159 by ankor@dixie-net.com(15667)   on 2013-01-06 21:04:17 (Show Source): You can put this solution on YOUR website!There are three equations all related, you should memorize all three of them Find distance dist = speed * time written as d = s * t or sometimes d = r * t (for rate) : Find Speed s = : With these three you should be able to calculate any unknown related to dist, speed and time
 Percentage-and-ratio-word-problems/698838: The denominator of a proper fraction is 1 less than twice the numerator. The difference between the digits of the numerator and denominator is 3. Find the fraction and its reciprocal.1 solutions Answer 431156 by ankor@dixie-net.com(15667)   on 2013-01-06 20:57:49 (Show Source): You can put this solution on YOUR website!The denominator of a proper fraction is 1 less than twice the numerator. The difference between the digits of the numerator and denominator is 3. Find the fraction and its reciprocal. : Since it is a proper fraction we know that d > n An equation for each statement : d = 2n - 1 and d - n = 3 d = (n+3) Replace d in the 1st equation n + 3 = 2n - 1 3 + 1 = 2n - n n = 4 then d = 4 + 3 d = 7 : is the fraction and the reciprocal:
 Numbers_Word_Problems/698836: chris collected toys for charity. he donated 3/4 to charity A and then 1/3 of the remaining to charity B. After the two donations, Chris had 10 toys left. How many did Chris originally collect?1 solutions Answer 431080 by ankor@dixie-net.com(15667)   on 2013-01-06 14:57:18 (Show Source): You can put this solution on YOUR website!chris collected toys for charity. he donated 3/4 to charity A and then 1/3 of the remaining to charity B. After the two donations, Chris had 10 toys left. How many did Chris originally collect? : let x the original number of toys : x - x = x after the first donation then after 1/3 of the remainder is donated you have: *x = 10 x = 10 2x = 12*10 2x = 120 x = 60 toys originally : : You can check this in the original equations
 Graphs/698842: Find two equations with graphs that' intersect at (3,-1). Show that (3,-1) makes both equations true.1 solutions Answer 431069 by ankor@dixie-net.com(15667)   on 2013-01-06 14:28:33 (Show Source): You can put this solution on YOUR website! Find two equations with graphs that' intersect at (3,-1). Show that (3,-1) makes both equations true. : Write two equations with difference slopes, but x1 = 3, y1 = -1 are the same Using the form: y - y1 = m(x - x1) : y - (-1) = -3(x - 3) y + 1 = -3x + 9 y = -3x + 9 - 1 y = -3x + 8; the 1st equation and y -(-1) = 2(x - 3) y + 1 = 2x - 6 y = 2x - 6 - 1 y = 2x - 7; the 2nd equation ; Graph these You can see they intersect at 3, -1 : YOu can prove this to yourself. Replace x with 3 in both equations and see if y = -1
 Travel_Word_Problems/698780: A professional cyclist travels 60km at an average speed of x km/hr Write down an expression in x to represent the time taken for this journey On the return journey the cyclist travelled at an average speed 5 km/hr slower Write down an expression in x to represent the time taken for this journey If the difference between the travelling times for both journeys was 2 hours write down an equation in terms of x to represent this and solve it to find x 1 solutions Answer 431066 by ankor@dixie-net.com(15667)   on 2013-01-06 14:12:36 (Show Source): You can put this solution on YOUR website!A professional cyclist travels 60km at an average speed of x km/hr Write down an expression in x to represent the time taken for this journey : On the return journey the cyclist travelled at an average speed 5 km/hr slower Write down an expression in x to represent the time taken for this journey ; If the difference between the travelling times for both journeys was 2 hours write down an equation in terms of x to represent this and solve it to find x - = 2 multiply x(x-5), resulting in: 60x - 60(x-5) = 2x(x-5) : 60x - 60x + 300 = 2x^2 - 10x A quadratic equation 0 = 2x^2 - 10x - 300 Simplify divide by 2 x^2 - 5x - 150 = 0 factors to: (x-15)(x+10) = 0 the positive solution is all we want here x = 15 km/hr : : : See if that checks out find the time at each speed 60/10 = 6 hrs 60/15 = 4 hrs -------------- dif of: 2 hrs
 Age_Word_Problems/698819: in 34 years, Tiffany will be 3 times as old as she is right now. How old is she?1 solutions Answer 431063 by ankor@dixie-net.com(15667)   on 2013-01-06 14:02:37 (Show Source): You can put this solution on YOUR website!in 34 years, Tiffany will be 3 times as old as she is right now. How old is she? : Let a = T's present age "in 34 years, Tiffany will be 3 times as old as she is right now." a + 34 = 3a 34 = 3a - a 34 = 2a a = 34/2 a = 17 yrs old now
 Radicals/698796: what is the answer with the solution to 3 square roots of 54 minus 2 square roots of 24 minus 1 square root of 96 plus 4 square roots of 63. Please i need help I've tried the problem and the answer doesn't look right.1 solutions Answer 431062 by ankor@dixie-net.com(15667)   on 2013-01-06 13:59:21 (Show Source): You can put this solution on YOUR website! 3 square roots of 54 minus 2 square roots of 24 minus 1 square root of 96 plus 4 square roots of 63. Assume it is: See what we can factor inside the radical, to reveal some perfect squares: Extract those square roots which is Like terms, 9 - 4 - 4 , using a calc: = 34.1985
 absolute-value/698602: Hi there! I am working on an absolute value lesson in my algebra book and there is a section where it says, "Describe and correct the error in solving the absolute value equation." The one I'm stuck on looks like this: |x-6|=-2 x-6=-2 or x-6=2 x=4 or x=8 I have looked at it for a long time and I still don't understand what the error is. You rewrite the original equation as two equations, positive and negative, and then you solve them. It looks correct to me! Could you help me figure out what the error is? I'm sure it's right there in front of me, but for some reason I just can't figure it out. Thank you!1 solutions Answer 430883 by ankor@dixie-net.com(15667)   on 2013-01-05 15:49:44 (Show Source): You can put this solution on YOUR website!I think the reason is, as the problem is written, it shows a negative value equal to an expression derived from inside the absolute brackets. Any value from an absolute has to be positive. : The correction could be |x - 6| = 2 then solve it like you did
 test/698303: what is the ratio 0.6:2.4 written in simplest form? 1 solutions Answer 430820 by ankor@dixie-net.com(15667)   on 2013-01-05 09:14:59 (Show Source): You can put this solution on YOUR website! what is the ratio 0.6:2.4 written in simplest form? Multiply by 10 to get rid of the decimals 6:24 Divide by 6 1:4 is the simplest form
 Travel_Word_Problems/698395: Paul made a round trip between two points A and B in 8 hours. His speed going up is 9 mph . His speed going down is 18 mph . His speed going on a level surface 12 mph . What is the distance in miles between A and B?1 solutions Answer 430670 by ankor@dixie-net.com(15667)   on 2013-01-04 16:40:25 (Show Source): You can put this solution on YOUR website!Paul made a round trip between two points A and B in 8 hours. His speed going up is 9 mph . His speed going down is 18 mph . His speed going on a level surface 12 mph. What is the distance in miles between A and B? : let h = the distance of the hill let f = the distance of the level surface : Write a time equation, time = dist/speed : up + lev + lev return + down = 8 hrs + + + = 8 multiply by 36 to get rid of the denominators, results 4h + 3f + 3f + 2h = 36(8) Combine like terms 6h + 6f = 288 simplify, divide by 6 h + f = 288/6 h + f = 48 miles, is the distance from A to B
 Linear-equations/698337: I feel really dumb, but I do not comprehend factoring at all. Maybe it's just that it's late, but how do I solve 15x^2 + 26x + 8 = 01 solutions Answer 430609 by ankor@dixie-net.com(15667)   on 2013-01-04 09:24:06 (Show Source): You can put this solution on YOUR website!solve 15x^2 + 26x + 8 = 0 Start by factoring 15 and 8 (5x + 4)(3x + 2) FOIL this, does (5*2)+(4*3) = 26, no; then try (5x + 2)(3x + 4) FOIL again, (5*4)+(2*3) does in fact, add up 26 (5x + 2)(3x + 4) = 0 5x = -2 x = -2/5 and 3x = 4 x = -4/3
 Numeric_Fractions/698080: Three times the first of three consecutive odd integers is 3 more than twice the third. Find the third integer?1 solutions Answer 430579 by ankor@dixie-net.com(15667)   on 2013-01-03 21:56:08 (Show Source): You can put this solution on YOUR website!Three odd integers: x, (x+2), (x+4) : Three times the first of three consecutive odd integers is 3 more than twice the third. 3x = 2(x+4) + 3 3x = 2x + 8 + 3 3x - 2x = 11 x = 11 is the first integer : You can Find the third integer?
 test/698060: if eight men working 8 hours per day for eight days can produce 8 grumpets how many grumpets can two men working 8 hours per day for four days produce? a)1 b)2 c)3 d)4 e)51 solutions Answer 430576 by ankor@dixie-net.com(15667)   on 2013-01-03 21:51:44 (Show Source): You can put this solution on YOUR website!if eight men working 8 hours per day for eight days can produce 8 grumpets Find how many man-hrs required to make one = 64 man-hrs : how many grumpets can two men working 8 hours per day for four days produce? = 1 grumpet
 test/698268: If the sum of a number and -5 is reduced by 7 the result is 15 less than three times the opposite of the number find the number1 solutions Answer 430574 by ankor@dixie-net.com(15667)   on 2013-01-03 21:35:04 (Show Source): You can put this solution on YOUR website!If the sum of a number and -5 is reduced by 7 the result is 15 less than three times the opposite of the number find the number : n = the number -n = it's opposite : n + (-5) - 7 = 3(-n) - 15 n - 12 = -3n - 15 n + 3n = -15 + 12 4n = -3 n = -3/4 n = -.75 : See if that works -.75 - 5 - 7 = 3(.75) - 15 -12.75 = 2.25 - 15 -12.75 = -12.75
 Age_Word_Problems/698229: Two trains, E and F travel along parallel tracks. Each track is 220 miles long. They begin their trips at the same time. Train E travels at a rate of 55 miles per hour and train F travels at a rate of 22 miles per hour. How many miles will train F have left to travel after train E completes its trip?1 solutions Answer 430572 by ankor@dixie-net.com(15667)   on 2013-01-03 21:27:08 (Show Source): You can put this solution on YOUR website!Two trains, E and F travel along parallel tracks. Each track is 220 miles long. They begin their trips at the same time. Train E travels at a rate of 55 miles per hour and train F travels at a rate of 22 miles per hour. How many miles will train F have left to travel after train E completes its trip? : Find how long it takes Train E to make the trip (220 mi) 220/55 = 4 hrs : Find how far train F travels in 4 hrs 4*22 = 88 mi then 220 - 88 = 132 mi to go for train F, when E completes the journey of 220 mi
 Proportions/698257: please help me solve the expression.7 7/9 divide 2 1/13 divided tried to change to an improper fraction first. they gave me 5,6,7 & 4 to possibily be equal to my problem.1 solutions Answer 430568 by ankor@dixie-net.com(15667)   on 2013-01-03 20:50:38 (Show Source): You can put this solution on YOUR website!7 7/9 divide 2 1/13 Improper fractions / Invert the dividing fraction, then multiply * = = 3
 Rate-of-work-word-problems/698256: Tom can sort 280 nails in 2 hours and jerry can sort 120 nails in 3 hours how long will it take them to both sort 700 nails1 solutions Answer 430566 by ankor@dixie-net.com(15667)   on 2013-01-03 20:38:45 (Show Source): You can put this solution on YOUR website! Tom can sort 280 nails in 2 hours and jerry can sort 120 nails in 3 hours how long will it take them to both sort 700 nails : Find the no. of nails per hr, each can sort Tom: 280/2 = 140 per hr Jer: 120/3 = 40 per hr : Let t = time (in hrs) required for both to sort 700 nails 140t + 40t = 700 180t = 700 t = 700/180 t = 3.89 hrs or 3 + .89(60) = 3 hrs 53 min