rates - floodgates - kaplan 800

[resilient]

I am trying to understand the logic and best approach to this question. Can someone please help. Stuart?

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains in 10 days, how many days does it take floodgate B alone to drain the reservoir?

a.4
b.5
c.6 2/3
d. 10
e. 12

qa is b


The solution explains that A will drain 1/3 of reserviour by multiplying 3 1/3 days and 1/10. I dont see the reasoning of this. How can multiplying those two give that A does 1/3 of the job.

[moneyman]

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains in 10 days, how many days does it take floodgate B alone to drain the reservoir?

a.4
b.5
c.6 2/3
d. 10
e. 12


According to the question,

1/A+1/B=1/t here 1/A is the work done by A in one day, 1/B is the work done by B in one day and 1/t is the total work done by both A and B in one day.

Subsititute the value of A and t we get,

1/10+/B=1/(10/3)

1/10+1/B=3/10 whcih equals 1/B=3/10-1/10=2/10=1/5

So we know that 1/B=1/5 which means that B will take 5 days to complete the job.

Hope it helps!!

[resilient]

Genius. PErfect. This was the approach I was trying to do but got lost somewhere and a bit insecure on my approach. I get it just set up the values logicaally and for the B value out. Perfect

Thanks a lot. DOes anyone have any place to point me to get more questions. I am running out of rate questions, they are getting fun and no longer impossible. Actually they are getting much easier.