Economist 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
Don't have the OA
I am interested in the approach.
I did:
10/4 - x/5 = 1/10 ( x = number of hours drain pipe is opened ). But I cant find the answer.
Imagine both the drain and the valve are on at the same time. You can use a formula here; I just convert each to the same amount of time (20 hours):
valve will fill 5 pools in 20 hours
drain will empty 4 pools in 20 hours
valve+drain will fill 1 pool in 20 hours
So we really have two 'workers' here; the valve, which fills one pool in 4 hours, is on for the first t hours, and the valve+drain combo, which fills one pool every 20 hours, which was on for the remaining 10 - t hours. While the valve was on, t/4 of the pool was filled, and while the valve+drain combo were on, (10-t)/20 of the pool was filled. Adding these, we must get 1 pool:
t/4 + (10-t)/20 = 1
5t + 10 - t = 20
4t = 10
t = 2.5
So the drain was turned on 2.5 hours after 1pm, or at 3:30pm.