Question

Three small pumps and a large pump are filling a tank. Each of the three small pumps works at \( \frac{2}{3} \) the rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

• A. \( \frac{4}{7} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{3}{4} \)

Hint:

When multiple pumps are working together, sum their individual rates to find the combined rate and use it to calculate the time taken.

Answer 1

The Correct Option is C

Let the rate of the large pump be \( L \). Then the rate of each small pump is \( \frac{2}{3}L \). The total rate of the four pumps working together is: \[ \text{Total rate} = L + 3 \times \frac{2}{3}L = L + 2L = 3L. \] The large pump alone would fill the tank in \( \frac{1}{L} \) time. The time taken by all four pumps together is: \[ \text{Time} = \frac{1}{3L}. \] Thus, the time taken is \( \frac{1}{3} \) of the time taken by the large pump alone. Therefore, the fraction of the time is \( \frac{2}{3} \).