During the first 18 minutes of a 1.0-hour trip, a car has an average speed of 11 m/s. What must the average speed of the car be during the last 42 minutes of the trip be if the car is to have an average speed of 21 m/s for the entire trip?
A)21 m/s
B)23 m/s
C)25 m/s
D)27 m/s
E)29 m/s

Question

Quizplus · Accepted Answer

The total distance traveled is the same for both the first 18 minutes and the last 42 minutes. Therefore, the average speed for the entire trip is the total distance traveled divided by the total time taken. The total time taken is 18 minutes + 42 minutes = 60 minutes = 1 hour. The total distance traveled is the average speed for the first 18 minutes multiplied by the time taken for the first 18 minutes plus the average speed for the last 42 minutes multiplied by the time taken for the last 42 minutes. Therefore, we have:```Average speed for the entire trip = (Average speed for the first 18 minutes * Time taken for the first 18 minutes + Average speed for the last 42 minutes * Time taken for the last 42 minutes) / Total time taken```Substituting the given values, we get:```21 m/s = (11 m/s * 18 minutes + Average speed for the last 42 minutes * 42 minutes) / 60 minutes```Solving for the average speed for the last 42 minutes, we get:```Average speed for the last 42 minutes = 25 m/s```Therefore, the average speed of the car during the last 42 minutes of the trip must be 25 m/s for the car to have an average speed of 21 m/s for the entire trip.

During the First 18 Minutes of a 1