Difference between revisions of "2011 AMC 10A Problems/Problem 15"

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Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 40 miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 0.02 gallons per mile. On the whole trip he averaged 55 miles per gallon. How long was the trip in miles?
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== Problem 15 ==
  
'''(A) 140  (B) 240  (C) 440  (D) 640  (E) 840'''
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Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first <math>40</math> miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of <math>0.02</math> gallons per mile. On the whole trip he averaged <math>55</math> miles per gallon. How long was the trip in miles?
  
== Solution ==
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<math>
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\mathrm{(A)}\ 140 \qquad
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\mathrm{(B)}\ 240 \qquad
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\mathrm{(C)}\ 440 \qquad
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\mathrm{(D)}\ 640 \qquad
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\mathrm{(E)}\ 840
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</math>
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== Solution 1 ==
  
 
We know that <math>\frac{\text{total miles}}{\text{total gas}}=55</math>. Let <math>x</math> be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is <math>0.02x</math>. The total distance traveled is <math>40+x</math>, so we get <math>\frac{40+x}{0.02x}=55</math>. Solving this equation, we get <math>x=400</math>, so the total distance is <math>400 + 40 = \boxed{440 \ \mathbf{(C)}}</math>.
 
We know that <math>\frac{\text{total miles}}{\text{total gas}}=55</math>. Let <math>x</math> be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is <math>0.02x</math>. The total distance traveled is <math>40+x</math>, so we get <math>\frac{40+x}{0.02x}=55</math>. Solving this equation, we get <math>x=400</math>, so the total distance is <math>400 + 40 = \boxed{440 \ \mathbf{(C)}}</math>.
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==Video Solution==
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https://youtu.be/HQmkIPpuIEc
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~savannahsolver
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== See Also ==
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{{AMC10 box|year=2011|ab=A|num-b=14|num-a=16}}
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{{MAA Notice}}

Revision as of 20:45, 9 January 2021

Problem 15

Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first $40$ miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of $0.02$ gallons per mile. On the whole trip he averaged $55$ miles per gallon. How long was the trip in miles?

$\mathrm{(A)}\ 140 \qquad \mathrm{(B)}\ 240 \qquad \mathrm{(C)}\ 440 \qquad \mathrm{(D)}\ 640 \qquad \mathrm{(E)}\ 840$

Solution 1

We know that $\frac{\text{total miles}}{\text{total gas}}=55$. Let $x$ be the distance the car traveled during the time it ran on gasoline, then the amount of gas used is $0.02x$. The total distance traveled is $40+x$, so we get $\frac{40+x}{0.02x}=55$. Solving this equation, we get $x=400$, so the total distance is $400 + 40 = \boxed{440 \ \mathbf{(C)}}$.

Video Solution

https://youtu.be/HQmkIPpuIEc

~savannahsolver

See Also

2011 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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

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