Problema Solution
One pump can drain a pool in 12 minutes. When a second pump is also used, the pool only takes 10 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump?
Answer provided by our tutors
The time the first pump alone takes to drain the pool = 12 minutes.
Then in one minute the fraction of draining done by it =1/12 of the pool.
Let the second pump take x minutes.
Then per minute capacity of draining by the second pump = 1/x of the pool.
Therefore, the joint capacity of the two pumps in one minute = 1/12 + 1/x.
But given that the two pumps drain jointly in 6 minutes ,in one minute they drain 1/6 of the pool.Therefore.
1/12 + 1/x = 1/6.=>
1/x = 1/6 - 1/12 = (2-1)/12 = 1/12
1/x = 1/12=>
x = 12 minutes .
Therefore the second pump alone takes 12 minutes to drain the pool.