Pipe A can fill the tank 5 times faster than pipe B, if pipe A and B together…

Concept

When two pipes fill the same tank together, their individual filling rates ADD. "k times faster" means a pipe's rate is k times the other's rate. The time taken to fill a tank equals (total work) divided by (rate), so a slower pipe needs proportionally more time than the combined effort.

Application

1. Let pipe B's rate be 1 unit per minute. Since A is 5 times faster, A's rate is 5 units per minute.

2. Working together, the combined rate is 5 + 1 = 6 units per minute.

3. They fill the tank in 50 minutes, so the tank's capacity is 6 units/min x 50 min = 300 units.

4. Pipe B alone fills 1 unit per minute, so it needs 300 units / 1 unit per minute = 300 minutes.

Cross-check

Pipe A alone would take 300 / 5 = 60 minutes. Using the combined-time formula, together they take (60 x 300) / (60 + 300) = 18000 / 360 = 50 minutes, which matches the given data.