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

## Problem 6

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?

$\textbf{(A) }50\qquad\textbf{(B) }70\qquad\textbf{(C) }80\qquad\textbf{(D) }90\qquad \textbf{(E) }100$

## Solution

Since Anh spends half an hour to drive 10 miles on the coastal road, his speed is $r=\frac dt=\frac{10}{0.5}=20$mph. His speed on the highway then is $60$mph. He drives $50$ miles, so he also drives $50$ minutes. The total amount of minutes spent on his trip is $30+50\implies \boxed{\textbf{(C) }80}$

Solution 2 Since Anh drives 3 times as fast on the highway, it takes him 1/3 of the time to drive 10 miles on the highway than on the coastal road. 1/3 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 80.