Difference between revisions of "2018 AMC 8 Problems/Problem 6"

m (Changed pronouns in solution to match pronouns in problem.)
(Use MathJax for solution 2)
 
(21 intermediate revisions by 13 users not shown)
Line 1: Line 1:
==Problem 6==
+
==Problem==
 
On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?
 
On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?
  
<math>\textbf{(A) }50\qquad\textbf{(B) }70\qquad\textbf{(C) }80\qquad\textbf{(D) }90\qquad \textbf{(E) }100</math>
+
[mathjax]\textbf{(A) }50\qquad\textbf{(B) }70\qquad\textbf{(C) }80\qquad\textbf{(D) }90\qquad \textbf{(E) }100[/mathjax]
  
==Solution==
+
==Solution 1==
  
Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is <math>r=\frac dt=\frac{10}{0.5}=20</math>mph. His speed on the highway then is <math>60</math>mph. He drives <math>50</math> miles, so he also drives <math>50</math> minutes. The total amount of minutes spent on his trip is <math>30+50\implies \boxed{\textbf{(C) }80}</math>
+
Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is [mathjax]r=\dfrac dt=\dfrac{10}{0.5}=20[/mathjax] mph. His speed on the highway then is [mathjax]60[/mathjax] mph. He drives [mathjax]50[/mathjax] miles, so he drives for 56 hours, which is equal to [mathjax]50[/mathjax] minutes (Note that 60 miles per hour is the same as 1 mile per minute). The total amount of minutes spent on his trip is [mathjax]30+50\implies \boxed{\textbf{(C) }80}[/mathjax].
 +
 
 +
==Solution 2==
 +
 
 +
Since Anh drives 3 times as fast on the highway, it takes him 13 of the time to drive 10 miles on the highway than on the coastal road. 13 of 30 is 10, and since he drives 50 miles on the highway, we multiply 10 by 5 to get 50. This means it took him 50 minutes to drive on the highway, and if we add the 30 minutes it took for him to drive on the coastal road, we would get (C) 80.
 +
 
 +
-UnstoppableGoddess
 +
(helped by qkddud)
 +
 
 +
== Video Solution (CRITICAL THINKING!!!)==
 +
https://youtu.be/qvdQCvTnC5A
 +
 
 +
~Education, the Study of Everything
 +
 
 +
==Video Solution==
 +
https://youtu.be/cGrnEwbV1QI
 +
 
 +
~savannahsolver
  
 
==See Also==
 
==See Also==

Latest revision as of 00:21, 4 April 2024

Problem

On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take?

(A) 50(B) 70(C) 80(D) 90(E) 100

Solution 1

Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is r=dt=100.5=20 mph. His speed on the highway then is 60 mph. He drives 50 miles, so he drives for 56 hours, which is equal to 50 minutes (Note that 60 miles per hour is the same as 1 mile per minute). The total amount of minutes spent on his trip is 30+50(C) 80.

Solution 2

Since Anh drives 3 times as fast on the highway, it takes him 13 of the time to drive 10 miles on the highway than on the coastal road. 13 of 30 is 10, and since he drives 50 miles on the highway, we multiply 10 by 5 to get 50. This means it took him 50 minutes to drive on the highway, and if we add the 30 minutes it took for him to drive on the coastal road, we would get (C) 80.

-UnstoppableGoddess (helped by qkddud)

Video Solution (CRITICAL THINKING!!!)

https://youtu.be/qvdQCvTnC5A

~Education, the Study of Everything

Video Solution

https://youtu.be/cGrnEwbV1QI

~savannahsolver

See Also

2018 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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 AJHSME/AMC 8 Problems and Solutions

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