One pump can fill a tank in 3 hours and another in 3.5 hours
so the rate at which both can half fill the tank is (1/3+1/3.5) => 13/21

Thus half of the tank can be filled in 21/13

so for filling the complete tank => 21/13*2 = 42/13 (D)

1st pump, 1/2 tank -> 3 hours, full -> 6 hours. This implies rate of 1/6 tank/hr
2nd pump, 1/2 tank -> 3.5 hours, full -> 7 hours. This implies rate of 1/7 tank/hr

Combined rate 1/6 + 1/7 = 13/42
For full tank -> 1/(13/42) = 42/13 = 3 3/13 -> D
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Hi All,

This question is an example of a "Work Formula" question; since it involves just two entities (in this case, water pumps), we can us the Work Formula to quickly get to the correct answer.

We're told that 2 different water pumps can fill HALF of a tank in 3 hours and 3.5 hours, respectively. That means that the two pumps could fill the ENTIRE tank in 6 hours and 7 hours, respectively.

Work = (A)(B)/(A+B)

A = 6 hours
B = 7 hours

(6)(7)/(6+7) = 42/13 = 3 3/13 hours to fill the entire tank when working together.

Final Answer:

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We are given that a water pump can fill half of a certain tank in 3 hours; thus, the rate of the pump is (1/2)/3 = 1/6. We are given that another pump can fill 1/2 of the same tank in 3½, or 7/2, hours. Thus, the rate of the second pump is (1/2)/(7/2) = 2/14 = 1/7. If we let t = the time it takes the two pumps working together to fill the entire tank, and if we let 1 equal the work (i.e., filling the entire tank) needed to be completed, we can create the following equation and determine t:

(1/6)t + (1/7)t = 1

Multiplying the entire equation by 42, we have:

7t + 6t = 42

13t = 42

t = 42/13 = 3 3/13

Answer: D
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