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# Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?

you must round the answer to the nearest minute

### 2 Answers by Expert Tutors

Chad W. | Experienced and Professional Tutor on a BicycleExperienced and Professional Tutor on a ...
4.9 4.9 (133 lesson ratings) (133)
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This is an example of a combined rates problem. Pump A has a rate of 0.20 tanks per hour. Pump B has a rate of 0.125 tanks per hour. Thus, their combined rate is 0.325 tanks per hour.

The reciprocal of the rate gives hours per tank.
1/0.325 = 3.0769 hours per tank
To convert this to minutes, multiply by 60.
(3.0769 hr/tank) * (60 min/hr) = 184.62 min/tank
We round this to the nearest minute. Thus, it takes about 185 minutes to fill the tank when the pumps work together.

The combined rate formula:
(time combined) = 1 / ( 1/(time A) + 1/(time B) )
Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
4.9 4.9 (178 lesson ratings) (178)
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A in one hour does 1/5
A in x hours does x/5

B in one hour does 1/8
B in x hours does x/8

x/5 + x/8 = 1     (the one complete tank)

Can you solve for x and answer?