A motorist makes a trip of 180 miles.For the first 90 miles she drives at a constant speed of 30 mph.At what constant speed must she drive the remaining distance if her average speed for the total trip is to be 40 mph?
A)45 mph
B)50 mph
C)52.5 mph
D)55 mph
E)60 mph

Question

Quizplus · Accepted Answer

To find the required speed for the second half of the trip, we first calculate the total time needed for the trip to have an average speed of 40 mph over 180 miles. This total time is 180 miles / 40 mph = 4.5 hours. The time taken for the first 90 miles at 30 mph is 90 miles / 30 mph = 3 hours. Therefore, the remaining time for the second half of the trip is 4.5 hours - 3 hours = 1.5 hours. To cover the remaining 90 miles in 1.5 hours, the motorist must drive at 90 miles / 1.5 hours = 60 mph.

A Motorist Makes a Trip of 180 Miles