Question

Worker A finishes the job in 10 hours; worker B finishes it in 12 hours, and worker C finishes it in 15 hours.

1. After A worked alone for two hours, and then B worked alone for 4 hours, how many hours will it take C alone to finish the remaining work?

It takes 40 minutes to fill a water tank, and 60 minutes to drain it.

2. If we try to fill the tank when empty while draining it for 1 minute, what fraction of the tank will be filled?

If they ask me that the tank is 2/3 full how will I find the minutes it will take to drain? Do I divided 60?

Answer 1

a=1/10, b=1/12, c=1/15 (these are the rates for each worker...)

1.)

2(1/10)+4(1/12)+t/15=1

1/5+1/3+t/15=1

(3+5+t)/15=1

3+5+t=15

8+t=15

t=7

So it would take c 7 hours to finish the job.

2.)

1/40-1/60

(3-2)/120

1/120

The drain rate is 1/60. So you will need to find t when the tank is empty, while starting at 2/3 capacity...

2/3-t/60=0

(40-t)/60=0

40-t=0

t=40

It would take 40 minutes to empty the tank when it is 2/3 full.