Fill the swimming pool
Two large and 1 small hoses can fill a swimming pool in 4 hours. One large and 3 small hoses can also fill the same swimming pool in 4 hours. How many minutes will it take 4 large and 2 small hoses to fill the swimming pool.(We assume that all large pumps are similar and all small pumps are also similar.)
The answer is 120.
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1 solution
If x is the time for the large hose to fill the pool alone, and y be the time for the small hose (in hr): then we can write the system:
2/x + 1/y = 1/4 (i)
1/x + 3/y = 1/4 (ii)
which solving for x and y gives x = 10 hr, y = 20 hr. Hence for four large hoses and two small hoses used together, the pool fills in time T hrs according to:
4/x + 2/y = 1/T (iii)
or 4/10 + 2/20 = 1/T;
1/2 = 1/T;
or T = 2 hr = 120 min.