Pump A can fill a tank in 6 hours. Pump B can fill the same tank in 4 hours. Working together at constant rates, how long do the two pumps take to fill the tank?
- A2 hours
- B2 hours 12 minutes
- C2 hours 24 minutes
- D2 hours 30 minutes
- E5 hours
Combined work: add rates, not times
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: C
Convert each time to a rate. Pump A fills 1/6 of the tank per hour, Pump B fills 1/4 per hour. Rates add when machines work together:
1/6 + 1/4 = 2/12 + 3/12 = 5/12 of the tank per hour.
Time is the reciprocal of the combined rate: 12/5 hours = 2.4 hours = 2 hours 24 minutes.
The classic errors:
- (E), 5 hours, comes from averaging 6 and 4. Two pumps working together must be faster than either one alone, so any answer above 4 hours is impossible on its face.
- (A) and (B) come from adding the fractions incorrectly, for example 1/6 + 1/4 = 1/5, which would give 5 hours, or from miscomputing the reciprocal.
Estimation check: alone, the faster pump needs 4 hours, so together they should need a bit more than half of that. 2 hours 24 minutes fits; 2 hours 12 minutes is suspiciously close to half of 4 hours exactly (that would require the slower pump to contribute nothing).