2009 AMC 8 Problem 6

Below is the professionally curated solution for Problem 6 of the 2009 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 8 solutions, or check the answer key.

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Concepts:rate unit conversion

Difficulty rating: 870

Steve's empty swimming pool will hold $24,000$ gallons of water when full. It will be filled by $4$ hoses, each of which supplies $2.5$ gallons of water per minute. How many hours will it take to fill Steve's pool?

$40$

$42$

$44$

$46$

$48$

Solution:

The $4$ hoses together fill the pool with $2.5 \cdot 4 = 10$ gallons of water per minute.

To fill $24,000$ gallons, it will take the hoses $24,000 \div 10 = 2,400$ minutes to fill the pool.

$2,400$ minutes is the same as $2,400 \div 60 = 40$ hours.

Thus, A is the correct answer.

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