Problem Solving

Q. Pumps A, B and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; Pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; And pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?

1. 1/3
2. 1/2
3. 2/3
4. 5/6
5. 1

Ans : E

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?

A. 1/3
B. 1/2
C. 2/3
D. 5/6
E. 1

I received a PM asking me to respond.

When the job is undefined, we can plug in a value for the job.

We should plug in a value that will make the math easy. To determine the rates for the various pumps, we'll be dividing the value of the job by the times given in the problem. Two of the times given are fractions. To divide by a fraction, we multiply by the reciprocal of the fraction. Thus, we should plug in a value that is divisible by the numerators of the fractions.

Plug in tank = 6.
Rate for A+B = w/t = 6/(6/5) = 5/hour.
Rate for A+C = w/t = 6/(3/2) = 4/hour.
Rate for B+C = w/t = 6/2 = 3/hour.
Combining the rates, we get:
(A+B) + (A+C) + (B+C) = 5+4+3.
2(A+B+C) = 12.
A+B+C = 6/hour.
Time for A+B+C = w/r = 6/6 = 1 hour.

The correct answer is E.

A&B fill in 6/5 hrs => in 1 hr they fill 5/6 of hte tank
A&C fill in 3/2 hrs => in 1 hr they fill 2/3 of hte tank
B&C fill in 2 hrs => in 1 hr they fill 1/2 of hte tank



If all work together for 1 hr then they can fill 5/6+2/3+1/2 of the tank => 2

since each has worked twice , it is 2/2 = 1 hr