Difference between revisions of "2009 AMC 8 Problems/Problem 6"
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| − | ==Problem== | + | ==Problem 6== |
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== | ||
| + | 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== | ||
| + | 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== | ||
| + | https://youtu.be/USVVURBLaAc?t=288 | ||
| + | |||
| + | ==Video Solution 2== | ||
| + | https://youtu.be/UkMGKf172E0 | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=5|num-a=7}} | {{AMC8 box|year=2009|num-b=5|num-a=7}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 07:23, 30 May 2023
Problem 6
Steve's empty swimming pool will hold 
gallons of water when full. It will be filled by 
hoses, each of which supplies 
gallons of water per minute. How many hours will it take to fill Steve's pool?
Solution
Each of the four hoses hose fills 
gallons of water. At the rate it goes at it will take 
minutes, or 
hours.
Solution 2
If all four hoses fill gallons a minute, every minute 
gallons would be added. Since every hour has 
minutes, 
gallons of water would be added every hour. 
hours.
~Trex226
Video Solution
https://youtu.be/USVVURBLaAc?t=288
Video Solution 2
~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. 
