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

Revision as of 18:30, 8 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

2020 AMC 10A (Problems • Answer Key • Resources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 8: / Line 8: @@
 ==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 <math>\boxed{\textbf{(E)}\ 26}</math>.
+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

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