Difference between revisions of "2020 AMC 10A Problems/Problem 4"

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<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 26 </math>
 
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 26 </math>
  
==Solution==
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==Solution 1==
Since the driver travels 60 miles per hour and each hour she uses 2 gallons of gasoline, she spends \$4 per hour on gas. If she gets \$0.50 per mile, then she gets \$30 per hour of driving. Subtracting the gas cost, her net rate of pay per hour is <math>\boxed{\textbf{(E)}\ 26}</math>.
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Since the driver travels <math>60</math> miles per hour and each hour she uses <math>2</math> gallons of gasoline, she spends <math>\$4</math> per hour on gas. If she gets <math>\$0.50</math> per mile, then she gets <math>\$30</math> per hour of driving. Subtracting the gas cost, her net rate of money earned per hour is <math>\boxed{\textbf{(E)}\ 26}</math>.
 
~mathsmiley
 
~mathsmiley
  
==Video Solution==
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==Solution 2 (longer)==
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The driver is driving for <math>2</math> hours at <math>60</math> miles per hour, she drives <math>120</math> miles. Therefore, she uses <math>\frac{120}{30}=4</math> gallons of gasoline. So, total she has <math>\$0.50\cdot120-\$2.00\cdot4=\$60-\$8=\$52</math>. So, her rate is <math>\frac{52}{2}=\boxed{\textbf{(E)}\ 26}</math>.
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~sosiaops
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==Video Solution 1==
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https://youtu.be/J-Ery8I0yAg
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==Video Solution 2==
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https://youtu.be/WUcbVNy2uv0
 
https://youtu.be/WUcbVNy2uv0
  
 
~IceMatrix
 
~IceMatrix
  
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==Video Solution 3==
 
https://www.youtube.com/watch?v=7-3sl1pSojc
 
https://www.youtube.com/watch?v=7-3sl1pSojc
  
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{{AMC10 box|year=2020|ab=A|num-b=3|num-a=5}}
 
{{AMC10 box|year=2020|ab=A|num-b=3|num-a=5}}
{{AMC12 box|year=2020|ab=A|num-b=2|num-a=4}}
 
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 02:49, 9 June 2022

The following problem is from both the 2020 AMC 12A #3 and 2020 AMC 10A #4, so both problems redirect to this page.

Problem

A driver travels for $2$ hours at $60$ miles per hour, during which her car gets $30$ miles per gallon of gasoline. She is paid $$0.50$ per mile, and her only expense is gasoline at $$2.00$ per gallon. What is her net rate of pay, in dollars per hour, after this expense?

$\textbf{(A)}\ 20\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 25\qquad\textbf{(E)}\ 26$

Solution 1

Since the driver travels $60$ miles per hour and each hour she uses $2$ gallons of gasoline, she spends $$4$ per hour on gas. If she gets $$0.50$ per mile, then she gets $$30$ per hour of driving. Subtracting the gas cost, her net rate of money earned per hour is $\boxed{\textbf{(E)}\ 26}$. ~mathsmiley

Solution 2 (longer)

The driver is driving for $2$ hours at $60$ miles per hour, she drives $120$ miles. Therefore, she uses $\frac{120}{30}=4$ gallons of gasoline. So, total she has $$0.50\cdot120-$2.00\cdot4=$60-$8=$52$. So, her rate is $\frac{52}{2}=\boxed{\textbf{(E)}\ 26}$. ~sosiaops

Video Solution 1

https://youtu.be/J-Ery8I0yAg

Video Solution 2

https://youtu.be/WUcbVNy2uv0

~IceMatrix

Video Solution 3

https://www.youtube.com/watch?v=7-3sl1pSojc

~bobthefam

https://youtu.be/Dj_DFoZO-xw

~savannahsolver

See Also

2020 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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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