Question

A pond is being drained by a pump. After 3 hours, the pond is half empty. A second pump is put into operation and together the two pumps finish emptying the pond in half an hour. How long would it take the second pump to drain the pond if it had to do the same job alone?

Answer 1

Answer:

The second pump to drain the pond if it had to do the same job alone is $\frac{3}{5}$ hour or 0.6 hour.

Step-by-step explanation:

Given : A pond is being drained by a pump. After 3 hours, the pond is half empty. A second pump is put into operation, and together the two pumps finish emptying the pond in half an hour.

To find : How long would it take the second pump to drain the pond if it had to do the same job alone?

Solution :

According to question,

Pump A drained in 3 hours.

So, Work done by pump in 1 hour is $\frac{1}{3}$

Together the two pumps finish emptying the pond in half an hour.

i.e. Pump A + Pump B drained in $\frac{1}{2}$ hour

Work done by pump in 1 hour is $\frac{1}{\frac{1}{2}}=2$ hour

The work done by pump B is $2-\frac{1}{3}$ hour.

The work done by pump B is $\frac{5}{3}$ hour.

So, Pump B drained in $\frac{3}{5}$ hour.

Therefore, The second pump to drain the pond if it had to do the same job alone is $\frac{3}{5}$ hour or 0.6 hour.

Answer 2

The first pump empties half the pond in 3 hours, so in 1/6 that time (1/2 hour), it empties (1/6)·(1/2) = 1/12 of the pond.

The second pump empties the other 5/12 of the pond in that half hour, so has a pumping rate of (1/2 h)/(5/12 pond) = (6/5 h)/pond.

The second pump could do the entire job alone in 1 hour and 12 minutes.