SOLUTION: It takes 3 pumps 8 hours to pump water out of a flooded basement. Find the time it takes each of them to pump water out of the basement by itself if it is known that the first pump

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes 3 pumps 8 hours to pump water out of a flooded basement. Find the time it takes each of them to pump water out of the basement by itself if it is known that the first pump      Log On


   

Question 645148: It takes 3 pumps 8 hours to pump water out of a flooded basement. Find the time it takes each of them to pump water out of the basement by itself if it is known that the first pump is
twice as fast as the second pimp and three times as fast as the third pump.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes 3 pumps 8 hours to pump water out of a flooded basement.
Find the time it takes each of them to pump water out of the basement by
itself if it is known that the first pump is twice as fast as the second
pimp and three times as fast as the third pump.
:
I am not sure how effective a pimp would be in this task.
:
Three pumps with times of: a, b, c
Let the completed job = 1 (an empty basement)
:
Write a shared work equation
8%2Fa + 8%2Fb + 8%2Fc = 1
:
"the first pump is twice as fast as the second"
b = 2a (b take 2 times as long as a)
:
three times as fast as the third pump.
c = 3a (c takes 3 times as long as a)
:
Replace b and c in the shared work equation
8%2Fa + 8%2F%282a%29 + 8%2F%283a%29 = 1
Multiply by 6a to clear the denominators, results:
6(8) + 3(8) + 2(8) = 6a
48 + 24 + 16 = 6a
88 = 6a
a = 88/6
a = 142%2F3 hrs working alone
then
b = 2(142%2F3) = 291%2F3 hrs working alone
and
c = 3(142%2F3) = 44 hrs working alone