SOLUTION: Elf #1 has made 20 toy trains today and can make 5 more per hour. Elf #2 has made 28 trains today and can make 3 more per hour. How many hours until both elves have made the same n
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-> SOLUTION: Elf #1 has made 20 toy trains today and can make 5 more per hour. Elf #2 has made 28 trains today and can make 3 more per hour. How many hours until both elves have made the same n
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Question 1012240: Elf #1 has made 20 toy trains today and can make 5 more per hour. Elf #2 has made 28 trains today and can make 3 more per hour. How many hours until both elves have made the same number of trains and how many trains will that be? Answer by Theo(13342) (Show Source):
x is the number of hours.
5x is the number of additional trains elf 1 can make in x hours.
3x is the number of additional trains elf 2 can make in x hours.
you want to know how many hours are required for each to make the same number of trains.
20 + 5x is the total number of trains elf 1 can make in x hours.
28 + 3x is the total number of trains elf 2 can make in x hours.
if you want the total number of trains each makes to be the same, then set 20 + 5x equal to 28 + 3x.
your equation is 20 + 5x = 28 + 3x.
solve for x in this equaiton and you should have your answer.
start with 20 + 5x = 28 + 3x.
subtract 20 from both sides of this equation and subtract 3x from both sides of this equation to get 5x - 3x = 28 - 20
combine like terms to get 2x = 8
divide both sides of this equation by 2 to get x = 4.
they should have built a total of the same number of trains in 4 houjrs.
elf 1 will have built a total of 20 + 5*4 = 40 trains.
elf2 will have built a total of 28 + 3*4 = 40 trains.
solution is good.
it will take 4 additional hours and they both will have made a total of 40 trains each.
