Jul
12
How long will it take to fill the pool if the drain, which could drain the pool in 15 hours, is left open?
July 12th, 2010 posted by
admin
The time required to fill a pool with a water hose is 30 hours. Using a pump the pool can be filled in 10 hours. How long will it take to fill the pool using a pump and 2 hoses? 6 hours
In the pool problem above how long would it take to fill the pool if the drain, which could drain the pool in 15 hours, is left open. Hint: the fill rates add and the drain rate subtracts.
Dee W says:
July 14th, 2010 at 11:38 pm
x/30 + x/10 + x/10 = 1
x + 3x + 3x = 30
7x = 30
x = 30/7 = 4 1/2 hours
(x/30 + x/10 + x/10) – x/15 = 1
x + 3x + 3x – 2x = 30
5x = 30
x = 6 hours
bsajoo says:
July 17th, 2010 at 9:51 pm
Let x be the capacity of the pool.
Then the filling rate by hose = x/30
And filling rate by pump = x/10
Time taken to fill by two hoses and one pump = x/ (x/30 +x/30 +x/10)
= 1 (5/30) = 6 hours
Let t be the time taken to fill the pool, with the drain opened.
Water pumped in during time t = (x/30 +x/30 +x/10) * t
Water drained during time t = (x/15) * t
We know, water pimped in – water drained = capacity of the pool
Hence (x/30 +x/30 +x/10) * t – (x/15) * t = x
So t/6 – t/15 = 1
That is, t = 10 hours