Question

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?

$50$

$70$

$80$

$90$

$100$

Answer: C

Concepts:distance rate and time unit conversion

Difficulty rating: 900

Video solution:

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Written solution:

Anh drove $10$ miles on the coastal road in $30$ minutes. Therefore, his speed on the coastal road (notated as $v_c$ ) is $\begin{align*}v_c&=\dfrac{10}{30}\\ &=\dfrac13.\end{align*}$ This is $\dfrac13$ mile per minute. Since he drives $3$ times as fast on the highway (i.e. $v_h=3v_c$ ), his highway speed is $3\cdot \dfrac13 = 1$ mile per minute. Armed with these two facts, we know that Anh drove for $30$ minutes on the coastal road, and he drove $50$ miles at $1$ mile per minute. This means it takes $50$ minutes to drive the $50$ miles on the highway.

As such, the total travel time is $50+30=80$ minutes.

Thus, the correct answer is C.

2018 AMC 8 Problem 6

Answer: C

Difficulty rating: 900

Video solution:

Written solution:

Problem 6 in Other Years