A full 10,000-gallon water tank will be emptied using two pumps.

Question

A full 10,000-gallon water tank will be emptied using two pumps. Pump A working by itself is used to drain 30 percent of the tank's total capacity, at which point Pump B is added to the job. If the entire job of emptying the tank takes 50 hours, and Pump A works at a rate of 100 gallons per hour, what is Pump B's rate, in gallons per hour?

A) 150
B) 200
C) 250
D) 500
E) 700

A) 150 
B) 200
C) 250
D) 500
E) 700

Abhishekgmat87 · Answer

Pump A rate - 100 gallons per hr
Pump A will take 10000/100 or 100 hr to empty the tank.

Pump A working alone to drain 30 % of tank capacity.

Time taken to drain 30 % or 3000 gallon will be 3000/100 = 30 hr

Pump A and Pump B will work together for remaining 20 hrs.

Pump A will drain 2000 gallons in 20 hr.

Pump B has to drain remaining 5000 gallons in 20 hr. 
Rate of pump B = 500/20 = 250

Option C

AndrewN · Answer

Hello, everyone. My own way of solving the problem involves a hybrid of logic and work/rate technique. I am posting in hopes that this information may prove useful to someone. To start, work out everything you can about Pump A:

drains 30 percent of 10,000 gallons by itself → drains 3,000 gallons   rate is 100 gallons per hour → takes 30 hours to drain 3,000 gallons

With this part figured out, we can begin to give shape to what must be true when Pumps A and B work together:

will drain 7,000 gallons together to empty the tank   must take 50 - 30, or 20 hours of working together to finish the job   combined rate will be 7,000 gallons divided by 20 hours → 350 gallons per hour

Now, you can solve using algebra, using  x  for the unknown rate at which Pump B contributes. (Remember to invert.)

A: 100 gallons/hour → 1/100
B:  x  gallons/hour → 1/ x 
A + B: (100 +  x ) gallons/hour → 1/(100 +  x )

\frac{1}{(100 + x)} = \frac{1}{350}

Cross-multiply:

350 = 100 + x

250 = x

The answer must be (C)  . Of course, there are many ways to solve such questions—entirely by algebra, plugging in the answers and checking—but the method above is fairly efficient.

Good luck with your studies, everyone.

- Andrew

rvgmat12 · Answer

First one takes 30 hours to fill 30% of capacity

10000 = 100*50 + x*20

x = 250

IanStewart · Answer

We know A works for 50 hours in total, draining 100 gallons per hour, so A drains 5000 gallons. B drains the remaining 5000 gallons, and since A works alone to drain 3000 gallons, A works alone for 30 hours, and B works for only 20 hours, so B must be draining 5000/20 = 250 gallons per hour.

bumpbot · Answer

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A full 10,000-gallon water tank will be emptied using two pumps.

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