Problem:
On a trip to the beach, Anh traveled miles on the highway and miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent minutes driving on the coastal road, how many minutes did his entire trip take?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Anh drove miles on the coastal road in minutes. Therefore, his speed on the coastal road (notated as ) is:
Since he drives times as fast on the highway (i.e., ), his speed on the highway is:
Armed with these two facts, we know that Anh drove for minutes on the coastal road, and he drove miles at a speed of mile per minute on the highway. This means it takes minutes to drive the miles on the highway. As such, the total travel time is:
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions