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 t

Question

1 month ago

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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 t

wo 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?

Mathematics

2 answers:

tester [12.3K] · Answer 1 · 2026-03-14T04:49:02+03:00

Answer:

The second pump alone would take $\frac{3}{5}$ hour or 0.6 hour.

Detailed explanation:

Given: A pond is draining with one pump. After 3 hours, it's half empty. A second pump starts, and together they finish emptying the pond in half an hour.

To find: How long would it take for the second pump to drain the pond alone?

Solution:

From the problem,

Pump A worked for 3 hours.

Thus, the output from the pump in one hour is

$\frac{1}{3}$

Together, the two pumps completed the emptying in half an hour.

That is Pump A + Pump B combined worked for hour $\frac{1}{2}$

The output from the pump in one hour is hour $\frac{1}{\frac{1}{2}}=2$

The work contributed by Pump B totals $2-\frac{1}{3}$ hour.

Thus,

Pump B would clear the pond in $\frac{5}{3}$ hour.

Therefore, The second pump would need $\frac{3}{5}$

hour or 0.6 hour to drain the pond alone.

tester [12.3K] · Answer 2 · 2026-03-14T04:47:22+03:00

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

The second pump eliminates the remaining 5/12 of the pond in that same half hour, implying a pumping rate of (1/2 h)/(5/12 pond) = (6/5 h)/pond.

The second pump could entirely drain the pond by itself in 1 hour and 12 minutes.