Difference between revisions of "2008 AMC 12A Problems/Problem 7"
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<math>\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 6\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 10</math> | <math>\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 6\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 10</math> | ||
| − | ==Solution== | + | ==Solution 1== |
It will take <math>\frac{1}{4}</math> of an hour or <math>15</math> minutes to get to shore. | It will take <math>\frac{1}{4}</math> of an hour or <math>15</math> minutes to get to shore. | ||
Since only <math>30</math> gallons of water can enter the boat, only <math>\frac{30}{15}=2</math> net gallons can enter the boat per minute. | Since only <math>30</math> gallons of water can enter the boat, only <math>\frac{30}{15}=2</math> net gallons can enter the boat per minute. | ||
| − | Since <math>10</math> gallons of water enter the boat each minute, LeRoy must bail <math>10-2=8</math> gallons per minute <math>\Rightarrow\mathrm{(D)}</math>. | + | Since <math>10</math> gallons of water enter the boat each minute, LeRoy must bail <math>10-2=8</math> gallons per minute <math>\Rightarrow\mathrm{(D)}</math>. |
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| + | ==Solution 2== | ||
| + | We set up the following equation, where <math>x</math> is the answer: | ||
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| + | <math>\frac{30}{10-x} = 15 \Rightarrow\mathrm{x=2}</math> so the answer is <math>\Rightarrow\mathrm{(D)}</math>. | ||
==See Also== | ==See Also== | ||
Revision as of 13:27, 25 October 2020
- The following problem is from both the 2008 AMC 12A #7 and 2008 AMC 10A #11, so both problems redirect to this page.
Contents
Problem
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?
Solution 1
It will take 
of an hour or 
minutes to get to shore.
Since only 
gallons of water can enter the boat, only 
net gallons can enter the boat per minute.
Since 
gallons of water enter the boat each minute, LeRoy must bail 
gallons per minute 
.
Solution 2
We set up the following equation, where 
is the answer:
so the answer is .
See Also
| 2008 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 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 AMC 12 Problems and Solutions | |
| 2008 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
