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

m (Video Solution 1)
 
(10 intermediate revisions by 8 users not shown)
Line 7: Line 7:
 
<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==
+
==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>.
+
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>.
 +
~mathsmiley
 +
 
 +
==Solution 2 (longer)==
 +
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>
 +
~sosiaops
 +
 
 +
==Video Solution 1==
 +
 
 +
https://youtu.be/J-Ery8I0yAg
 +
 
 +
==Video Solution 2==
  
==Video Solution==
 
 
https://youtu.be/WUcbVNy2uv0
 
https://youtu.be/WUcbVNy2uv0
  
 
~IceMatrix
 
~IceMatrix
 +
 +
==Video Solution 3==
 +
https://www.youtube.com/watch?v=7-3sl1pSojc
 +
 +
~bobthefam
 +
 +
https://youtu.be/Dj_DFoZO-xw
 +
 +
~savannahsolver
  
 
==See Also==
 
==See Also==

Latest revision as of 22:50, 1 May 2021

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
2020 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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

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

Invalid username
Login to AoPS