Question

A car travels an average of 70 miles per hour for the first 5 hours of a 9 hour car trip. The car then hit traffic and had to travel an average of 25 miles per hour for the rest of the 9-hour trip. What is the average (arithmetic mean) speed in miles per hour during this trip?

Answer 1

The average speed of a car during a 9-hour trip, consisting of two parts with different speeds, is calculated by dividing the total distance traveled by the total time of the trip. In this case, the car travels a total of 450 miles over 9 hours, resulting in an average speed of 50 miles per hour.

Step-by-step explanation:

The student is asking how to calculate the average speed for a two-part car trip with different speeds for each part. To find this, we use the formula for average speed, which is the total distance traveled divided by the total time of the trip.

In the first part of the trip, the car travels at 70 miles per hour for 5 hours, so the distance covered is (70 miles/hour) × (5 hours) = 350 miles. In the remaining 4 hours (since the entire trip is 9 hours), the car travels at 25 miles per hour, so the distance covered is (25 miles/hour) × (4 hours) = 100 miles.

The total distance for the whole trip is 350 miles + 100 miles = 450 miles.

The total time of the trip is 9 hours. Therefore, the average speed of the car for the entire trip is:

Vavg = Total Distance / Total Time

Vavg = 450 miles / 9 hours

Vavg = 50 miles/hour

So, the average speed during the 9-hour trip is 50 miles per hour.