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Difference between revisions of "2009 AMC 8 Problems/Problem 6"

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==Problem 6==
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Steve's empty swimming pool will hold <math> 24,000</math> gallons of water when full. It will be filled by <math> 4</math> hoses, each of which supplies <math> 2.5</math> gallons of water per minute. How many hours will it take to fill Steve's pool?
 
Steve's empty swimming pool will hold <math> 24,000</math> gallons of water when full. It will be filled by <math> 4</math> hoses, each of which supplies <math> 2.5</math> gallons of water per minute. How many hours will it take to fill Steve's pool?
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<math> \textbf{(A)}\  40  \qquad
 
<math> \textbf{(A)}\  40  \qquad
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\textbf{(D)}\  46  \qquad
 
\textbf{(D)}\  46  \qquad
 
\textbf{(E)}\  48</math>
 
\textbf{(E)}\  48</math>
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==Solution==
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Each of the four hoses hose fills <math>24,000/4 = 6,000</math> gallons of water. At the rate it goes at it will take <math>6,000/2.5 = 2400</math> minutes, or <math>\boxed{\textbf{(A)}\ 40}</math> hours.
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==Solution 2==
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If all four hoses fill <math>2.5</math> gallons a minute, every minute <math>10</math> gallons would be added. Since every hour has <math>60</math> minutes, <math>600</math> gallons of water would be added every hour. <math>24000/600=\boxed{\textbf{(A)}\ 40}</math> hours.
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~Trex226
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==Video Solution==
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https://youtu.be/USVVURBLaAc?t=288
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==Video Solution 2==
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https://youtu.be/UkMGKf172E0
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~savannahsolver
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==See Also==
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{{AMC8 box|year=2009|num-b=5|num-a=7}}
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{{MAA Notice}}

Latest revision as of 07:23, 30 May 2023

Problem 6

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?

$\textbf{(A)}\ 40 \qquad \textbf{(B)}\ 42 \qquad \textbf{(C)}\ 44 \qquad \textbf{(D)}\ 46 \qquad \textbf{(E)}\ 48$

Solution

Each of the four hoses hose fills $24,000/4 = 6,000$ gallons of water. At the rate it goes at it will take $6,000/2.5 = 2400$ minutes, or $\boxed{\textbf{(A)}\ 40}$ hours.

Solution 2

If all four hoses fill $2.5$ gallons a minute, every minute $10$ gallons would be added. Since every hour has $60$ minutes, $600$ gallons of water would be added every hour. $24000/600=\boxed{\textbf{(A)}\ 40}$ hours.

~Trex226

Video Solution

https://youtu.be/USVVURBLaAc?t=288

Video Solution 2

https://youtu.be/UkMGKf172E0

~savannahsolver

See Also

2009 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 5 		Followed by
Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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