Correct Method for Rate Problem?

[bml1105]

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains the reservoir 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

OA: B







I solved it the following way. The book explained it differently and I just want to make sure my method is correct and I didn't just get lucky.

A ---> R = 1/10 T = 10 days W = 1 reservoir so 1/10 x 10 = 1

A&B ---> R x (10/3) = 1 so AB rate = 3/10

find B ---> AB Rate - A Rate = B Rate so 3/10 - 1/10 = 2/10

Time for B = T ---> (2/10) x T = 1 so T = (10/2) = 5 days

[Brent@GMATPrepNow]

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains the reservoir 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

OA: B







I solved it the following way. The book explained it differently and I just want to make sure my method is correct and I didn't just get lucky.

A ---> R = 1/10 T = 10 days W = 1 reservoir so 1/10 x 10 = 1

A&B ---> R x (10/3) = 1 so AB rate = 3/10

find B ---> AB Rate - A Rate = B Rate so 3/10 - 1/10 = 2/10

Time for B = T ---> (2/10) x T = 1 so T = (10/2) = 5 days

Your method is perfect!!

Cheers,
Brent

[Brent@GMATPrepNow]

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains the reservoir 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

I'd like to expand on your solution to show others exactly what your did.

For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let's use these rules to solve the question. . . .

Floodgate A alone drains the reservoir in 10 days
Applying rule #1, we know that floodgate A can complete 1/10 of the job in ONE DAY.

Floodgates A and B drain the reservoir in 3 1/3 days
In other words, floodgates A and B drain the reservoir in 10/3 days
Applying rule #1, we know that floodgates A and B can complete 3/10 of the job in ONE DAY.

In ONE DAY, A & B complete 3/10 of the job
In ONE DAY, A completes 1/10 of the job
So, in ONE DAY, B completes 2/10 of the job

If B completes 2/10 of the job in 1 day, we can apply rule #2 to conclude that floodgate B completes the ENTIRE job in [spoiler]10/2[/spoiler] days (or 5 days).

Answer: B

Cheers,
Brent

[GMATGuruNY]

When both floodgates A and B are open, a reservoir drains in 3 1/3 days. If floodgate A alone drains the reservoir 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

Let the reservoir = 10 liters.

Since A and B together take 10/3 days to drain the reservoir, the combined rate for A and B = w/t = 10/(10/3) = 3 liters per day.
Since A alone takes 10 days to drain the reservoir, A's rate alone = w/t = 10/10 = 1 liter per day.
Thus, B's rate alone = (combined rate for A and B together) - (A's rate alone) = 3-1 = 2 liters per day.
At a rate of 2 liters per day, the time for B alone to drain the reservoir = w/r = 10/2 = 5 days.

The correct answer is B.

[theCodeToGMAT]

10/3 days

A = 10 days
B = ?

1/10 + 1/B = 3/10
1/B = 1/5
B = 5
[spoiler]
{B}[/spoiler]