Hose A takes 2 days to fill a pool, hose B takes 3 days to f

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Anaira Mitch: Master | Next Rank: 500 Posts; Posts: 235; Joined: Wed Oct 26, 2016 9:21 pm; Thanked: 3 times; Followed by:5 members

Hose A takes 2 days to fill a pool, hose B takes 3 days to f

by Anaira Mitch » Tue Oct 31, 2017 10:32 pm

Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

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Source: Beat The GMAT — Problem Solving | Tue Oct 31, 2017 10:32 pm

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by GMATGuruNY » Wed Nov 01, 2017 3:00 am

Anaira Mitch wrote:Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

Let the pool = 6 liters.
Since A takes 2 days to fill the 6-liter pool, A's rate = w/t = 6/2 = 3 liters per day.
Since B takes 3 days to fill the 6-liter pool, B's rate = w/t = 6/3 = 2 liters per day.
Since C takes 6 days to fill the 6-liter pool, C's rate = w/t = 6/6 = 1 liter per day.

All three hoses are used to fill the first one-third of the pool.
Combined rate for A+B+C = 3+2+1 = 6 liters per day.
Time for A+B+C to fill 1/3 of the 6-liter pool = (1/3 of 6)/(combined rate for A+B+C) = 2/6 = 1/3 day.

Hose A and hose C continue until it is two-thirds full.
Combined rate for A+C = 3+1 = 4 liters per day.
Time for A+C to fill another 1/3 of the 6-liter pool = (1/3 of 6)/(combined rate for A+C) = 2/4 = 1/2 day.

Hose A continues until the pool is full.
Time for A to fill the remaining 1/3 of the 6-liter pool = (1/3 of 6)/(A's rate) = 2/3 day.

Total time = (1/3 day) + (1/2 day) + (2/3 day) = 1.5 days.

The correct answer is A.

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by Scott@TargetTestPrep » Thu Nov 02, 2017 4:07 pm

Anaira Mitch wrote:Hose A takes 2 days to fill a pool, hose B takes 3 days to fill a pool, and hose C takes 6 days to fill a pool. All three hoses are used to fill the first one-third of the pool, at which time hose B stops working and hose A and hose C continue until it is two-thirds full. At that point, hose C stops working and hose A continues until the pool is full. How long did it take to fill the entire pool?

a) 1.5
b) 2.5
c) 3.5
d) 4.5
e) 1.2

The rates of hose A, B, and C, respectively, are 1/2, 1/3, and 1/6.

We can let t = the time they work together, and thus the time it takes them to fill 1/3 of the pool is the following:

(1/2)t + (1/3)t + (1/6)t = 1/3.

Multiplying by 6, we have:

3t + 2t + t = 2

6t = 2

t = 1/3 hour

Next, we can let t = the time A and C work together, and thus the time it takes them to fill 1/3 of the pool is:

(1/2)t + (1/6)t = 1/3

Multiplying by 6, we have:

3t + t = 2

4t = 2

t = 1/2 hour

Finally, hose A completes the last 1/3 of the pool. We can let t = the time that A works:

(1/2)t = 1/3

t/2 = 1/3

3t = 2

t = 2/3

So, the total time is 1/3 + 1/2 + 2/3 = 2/6 + 3/6 + 4/6 = 9/6 = 3/2 = 1.5 hours.

Answer: A

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