One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 48 minutes, the slower pipe alone will be able to fill the tank in:

Correct — A. Let the slower pipe take x minutes on its own.

Rate of slower pipe = 1⁄x
Four times as fast means four times the rate, so faster pipe = 4⁄x
Combined rate = 1⁄x + 4⁄x = 5⁄x

Together they finish in 48 minutes, so 5⁄x = 1⁄48
x = 5 × 48 = 240 minutes → option (a).

Why the others are wrong

• (b)
  144 minutes — 144 is 3 × 48, the answer if the faster pipe were only twice as fast (1⁄x + 2⁄x = 3⁄x). The stem says four times, so the combined rate is 5⁄x.
• (c)
  192 minutes — 192 is 4 × 48. It solves 4⁄x = 1⁄48 and so drops the slower pipe's own contribution of 1⁄x, which has to be added in.
• (d)
  288 minutes — 288 is 6 × 48, which needs a combined rate of 6⁄x, that is a pipe five times as fast. Four times as fast gives 4⁄x, making the sum 5⁄x.

Work questions are rate questions. A pipe that fills a tank in t minutes works at 1⁄t tanks per minute, and rates add when pipes run together.

Four times as fast describes the rate, not the time. The fast pipe runs at 4⁄x while the slow one runs at 1⁄x, so together they run at 5⁄x.

Setting that equal to 1⁄48 gives the slower pipe's time straight away, with no need to find the faster pipe first.

Key facts

• A pipe filling a tank in t minutes has rate 1⁄t, and rates of pipes working together simply add.
• Four times as fast means four times the rate and therefore a quarter of the time, so the faster pipe takes 60 minutes.
• When two rates are in the ratio 1 : 4, the slower pipe alone takes 5 times the joint time.

Common traps

• Multiplying 48 by 4 instead of by 5, which leaves out the slower pipe's own 1⁄x.
• Solving for the faster pipe, 60 minutes, when the question asks for the slower one.
• Reading four times as fast as four times the time.

No directly related past PYQ was found.