Difference between revisions of "2008 AMC 12A Problems/Problem 7"

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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?
 
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?
  
<math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 10</math>
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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>
  
 
==Solution==  
 
==Solution==  
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 <math>10</math> gallons of water enter the boat per min, LeRoy must bail <math>10-2=8</math> gallons per minute <math>\Rightarrow D</math>.  
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It will take <math>\frac{1}{4}</math> of an hour or <math>15</math> minutes to get to shore.
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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.
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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>.  
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2008|num-b=6|num-a=8|ab=A}}
 
{{AMC12 box|year=2008|num-b=6|num-a=8|ab=A}}

Revision as of 23:08, 25 April 2008

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?

$\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 6\qquad\mathrm{(D)}\ 8\qquad\mathrm{(E)}\ 10$

Solution

It will take $\frac{1}{4}$ of an hour or $15$ minutes to get to shore.

Since only $30$ gallons of water can enter the boat, only $\frac{30}{15}=2$ net gallons can enter the boat per minute.

Since $10$ gallons of water enter the boat each minute, LeRoy must bail $10-2=8$ gallons per minute $\Rightarrow\mathrm{(D)}$.

See Also

2008 AMC 12A (ProblemsAnswer KeyResources)
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
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