SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS ONE??? I need to drain a pool. I know one pump can drain the pool in 8min and if I use a second pump I can drain the pool in 4min. The problem

Algebra ->  Rate-of-work-word-problems -> SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS ONE??? I need to drain a pool. I know one pump can drain the pool in 8min and if I use a second pump I can drain the pool in 4min. The problem      Log On


   

Question 194440: CAN SOMEONE PLEASE HELP ME WITH THIS ONE???
I need to drain a pool. I know one pump can drain the pool in 8min and if I use a second pump I can drain the pool in 4min. The problem is the first pump is being used so I can only use the second pump. So I need to know how long it will take me to drain the pool using only the second pump?
I've tried a few different ways to solve this and nothing comes up right..Thank you, thank you, thank you...
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I need to drain a pool. I know one pump can drain the pool in 8min and if I use a second pump I can drain the pool in 4min. The problem is the first pump is being used so I can only use the second pump. So I need to know how long it will take me to drain the pool using only the second pump?
:
Actually you can just look at this and see the answer is 8 min for the 2nd pump also,
however, that will not always be the case, here is a method that will work for any shared work problem
:
Let t = time required for the 2nd pump to drain the pool by itself
:
Let the completed job = 1; (drained pool)
:
Write the equation for the two pumps working together.
:
Each pump does a fraction of the job, those two fraction must add up to 1
4%2F8 + 4%2Ft = 1
multiply the equation by 8t
8t*4%2F8 + 8t*4%2Ft = 8t(1)
cancel out the denominators and you have:
4t + 8(4) = 8t
4t + 32 = 8t
32 = 8t - 4t
32 = 4t
t = 32%2F4
t = 8 min, both pumps pump at the same rate.