# MATH AGAIN?

One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days. How long will it take the two pumps, working together, to empty the pool?

The first pump's rate is

1/5

The second pump's rate is

1/8

The combined pumps rate is

13/40

It will take the two pumps

days to empty the pool together. =

### 10 Answers

- geezerLv 75 months ago
If the combined pumps rate is 13/40 ..

the time will be 40/13 days ..

3 1/13 days ..

3 days and almost 2 hours (1/12 would be exactly 2 hours)

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- sepiaLv 75 months ago
One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days.

How long will it take the two pumps, working together, to empty the pool?

The first pump's rate is 1/5. The second pump's rate is 1/8.

The combined pumps rate is 13/40

It will take the two pumps 3.07..days to empty the pool together.

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- nbsaleLv 65 months ago
Pay attention to the units. What are the units in a rate of "1/5"? It's one pool per 5 days.

So when you add the rates (the proper thing to do), you get 13/40, meaning 13 pools in 40 days, or since 13/40 = 1/(40/13), it's one pool per 40/13 days = 3 1/13 days = 3.076923... days (last 6 digits repeat).

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- Φ² = Φ+1Lv 75 months ago
The first pump could empty the pool 8 times in 40 days, and the second pump could empty the pool 5 times in 40 days.

Together they could empty the pool 13 times in 40 days, so (dividing through by 13) it will take the two pumps 40/13

days to empty the pool together.

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- SteveRenoLv 45 months ago
"One pump can empty a pool in 5 days, whereas a second pump can empty the pool in 8 days."

"How long will it take the two pumps, working together, to empty the pool?"

(5*8) / (5+8) = 40/13 days (about 3 and 1/13 day)

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- Anonymous5 months ago
In one day the first pump can empty 1/5 of the pool.

In one day, the second pump can empty 1/8 of the pool.

In one day, both pumps can empty 1/5 + 1/8 = 13/40 of the pool.

time = 1 / (13/40) = 40/13 days. A little over 3 days.

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