Rate Problems: More than One Worker - Combined Rates
Pipe _A_ fills a pool with a total volume of 3,600 liters at a rate of 30 liters per minute. Working alone, Pipe _B_ fills one-third of the pool in 6 hours. Working together, how long will it take both pipes to fill the pool?
Correct.
Second step: combine the rates.
>Rate $$A+B = 1{,}800 + 200 = 2{,}000$$ Liters per hour
Last step: now find the missing value using the combined rate in the __Work Table__.
| Rate | Time | Work |
|-------|------|-------|
| 2,000 | | 3,600 |
>$$\displaystyle \text{Time} = \frac{3{,}600}{2{,}000}=\frac{36}{20}=1\frac{8}{10} \text{ hour} $$
> $$\displaystyle= 1 \text{ hour} +\frac{8}{10}\times 60 \text{ minutes} = 1 \text{ hour} + 48 \text{ minutes}$$
Thus, the correct answer is 1 hour and 48 minutes.
Incorrect.
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Incorrect.
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You may have gotten this answer by missing out on a critical unit conversion! Go back to the question, and this time read more carefully.
Incorrect.
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Incorrect.
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First step: calculate the rate of each pipe.
Pipe _A_: The rate is given as 30 liters per minute. However, the rest of the question deals with rate in liters per hour, so a unit conversion is required here. Since 60 minutes is 1 hour, multiply by $$\frac{60 \text{ minutes}}{1 \text{ hour}}$$:
>30 Liters per minute $$\displaystyle \require{cancel} = \frac{30 \text{ Liters}}{1 \cancel{\text{ minute}}} \times \frac{60 \cancel{\text{ minutes}}}{1 \text{ hour}} $$
> $$\displaystyle = \frac{30\times60 \text{ Liters}}{1 \text{ hour}} = 1{,}800$$ Liters per hour
Pipe _B_: Calculate its rate using the data that it takes 6 hours to fill $$\frac{1}{3}$$ of the pool (sized 3,600 liters) with pipe _B_. Place that data in the __Work Table__.
| Rate | Time | Work |
|------|------|-------------------------------|
| | 6 | $$\frac{3{,}600}{3}=1{,}200$$ |
>Rate $$B = \frac{1{,}200}{6} = 200$$ Liters per hour
12 hours and 30 minutes
9 hours and 12 minutes
2 hours and 36 minutes
1 hour and 48 minutes
1 hour and 30 minutes
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