work problem

[rehab-299]

pump A can drain container in 3 hours, B can drain it in 2 hours and C can fill a full container in 6 hour opening A,B,C togather, if a container has full water, how many times does it drain the container will be half-full?

A)30 minutes
B) 45 minutes
C) 50 minutes
D) 60 mintes
E) 72 mintes

[2amitprakash]

Find the rates for all 3:
Pump A will drain 1/3 of container in 1 hour
Pump B will drain 1/2 of container in 1 hour
Pump C will drain 1/6 of container in 1 hour.

So combined A+B+C will drain (1/3+1/2+1/6=1) container in 1 hour.

So 1/2 of container will be drained in 1/2 hour = 30 minutes. Answer is A.
Correct answer in later post. Earlier misread the problem

[rehab-299]

the answer is B

[2amitprakash]

Sorry to misread your problem in hurry...my bad. The logic remains same-
Find the rates for all 3:
Pump A will drain 1/3 of container in 1 hour
Pump B will drain 1/2 of container in 1 hour
Pump C will fill 1/6 of container in 1 hour.

So combined A+B+C will drain (1/3+1/2-1/6=4/6) container in 1 hour. Notice the negative sign for opposite action.

So 1/2 of container will be drained in [(1/2)*(6/4)] hours = 45 minutes. Answer is B.

[RonPurewal]

Sorry to misread your problem in hurry...my bad. The logic remains same-
Find the rates for all 3:
Pump A will drain 1/3 of container in 1 hour
Pump B will drain 1/2 of container in 1 hour
Pump C will fill 1/6 of container in 1 hour.

So combined A+B+C will drain (1/3+1/2-1/6=4/6) container in 1 hour. Notice the negative sign for opposite action.

So 1/2 of container will be drained in [(1/2)*(6/4)] hours = 45 minutes. Answer is B.

nicely done.

[sachin.w]

So combined A+B+C will drain (1/3+1/2-1/6=4/6) container in 1 hour. Notice the negative sign for opposite action.

So 1/2 of container will be drained in [(1/2)*(6/4)] hours = 45 minutes. Answer is B.

Shouldn't it be 1/2 * 4/6 hours?
Combined it will be drained 4/6 th in 1 hour. So in half an hour, half of it will be drained right?

[RonPurewal]

Shouldn't it be 1/2 * 4/6 hours?
Combined it will be drained 4/6 th in 1 hour. So in half an hour, half of it will be drained right?

the problem here is that 4/6 is not a number of hours; it's a fraction of a container.
we can drain 4/6 of a container in 1 hour -- which means that it will take 6/4 hour to drain the entire container.

you can avoid this kind of mistake in the future by actually writing the units next to all numerical figures.
if your scratch paper actually says "4/6 container", it's going to be nearly impossible for you to make the mistake of thinking that 4/6 is a number of hours.

[sachin.w]

I get it now. :) Thanks! Fortunate to have Manhattan forums!

[tim]

:)