Problem Solving

A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

* at 2:00 pm
* at 2:30 pm
* at 3:00 pm
* at 3:30 pm
* at 4:00 pm

please help. I have difficult with word problem.

Before the drain was opened, the pool was only filled
no drainage

so, let the time period for only fill be t

so time required to fill with drain open = (1/4 - 1/5)*(10-t)

I have taken +ve for filling and -ve for drain.

here 10-t because=> 11pm-1 pm =10
and t was the time when the pipe has already been running.

now apply the equations of time and work

(1/4)*t + (1/4 - 1/5)*(10-t) = 1

t = 2.5

time started at 1pm

so, total time will be

1pm +2.5 = 3:30 pm

Hope this helps

nhai2003 wrote:A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?

* at 2:00 pm
* at 2:30 pm
* at 3:00 pm
* at 3:30 pm
* at 4:00 pm

please help. I have difficult with word problem.

If both are opened at the same time it takes 20 hours to fill

t/4-t/5=1
t=20
But the problems says it is filled in 10 hours. So

10/4-t/5=1
t=7.5

Only D 3:30PM satisfies.
From 11PM-3:30=7.5