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?

$50$

$70$

$80$

$90$

$100$

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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: $\begin{align*}v_c&=\dfrac{10\text{miles}}{30 \text{minutes}}\\ &= \dfrac{1\text{mile}}{3 \text{minutes}}\\ &=\dfrac13 \dfrac{\text{miles}}{\text{minute}}.\end{align*}$ Since he drives $3$ times as fast on highway (i.e. $v_h=3v_c$ ), he drives at a speed of $3\cdot \dfrac13 \dfrac{\text{miles}}{\text{minute}} = 1 \dfrac{\text{miles}}{\text{minute}}$ on the highway. 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

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Problem 6 in Other Years