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Question 1205672: 8 builders can build a house in 40 days, how long will it take for 2 builders to build a house?
Found 4 solutions by Theo, josgarithmetic, greenestamps, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p * r * t = q
p = number of people working on the project
r = the average rate that each person works at
t is the time
q is the quantity.
in this problem, .....
p = 8
r = what you want to find.
t is 40 days
q is 1 house
formula becomes 8 * r * 40 = 1
simplify to get 320 * r = 1
solve for r to get r = 1/320
when 2 workers are working, the formula becomes 2 * r * t = 1
when r = 1/320, the formula becomes 2 * 1/320 * t = 1
simplify to get 2/320 * t = 1
solve for t to get t = 320/2 * 1 = 160 days.
it takes 8 workers 40 days to finish the house.
it takes 2 workers 160 days to finish the house.
each worker finishes an average of 1/320 of the house in 1 day.
you can also work this as an inverse variation type problem, if you know that is the relationship necessary to solve a problem such as this.
it's an inverse variation type problem because there is an inverse relationship between the people working on the house and the time it takes to complete the house.
the more workers working on the house, the less time it takes to complete the house.
if you solve it that way, then the basic formula is y = k / x.
y is 40 and x is 8, so the formula becomes 40 = k / x
k is the constant of variation.
solve for k to get k = 320.
when x = 2, the formula becomes y = 320 / 2 = 160.
Answer by josgarithmetic(39620)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have received two responses showing rather lengthy formal solutions to the problem.
You can find the answer quickly and easily by using logical reasoning.
2 builders instead of 8 means there are 1/4 as many workers, so the time required is going to be 4 times as much.
ANSWER: 4*40 = 160 days
Answer by ikleyn(52809)  (Show Source):
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