Question

A bus traveled on a level road for 4 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on the level road if the entire trip was 400 miles.

Answer 1

Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:

distance = speed × time = s × 4

Similarly, the distance traveled on the level road is:

distance = speed × time = (s + 20) × 4

Since the entire trip was 400 miles, we can write:

4s + 4(s + 20) = 400

Simplifying this equation, we get:

8s + 80 = 400

8s = 320

s = 40

Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.

To check that this solution is correct, we can calculate the distance traveled on each road:

distance on winding road = 40 × 4 = 160 miles

distance on level road = 60 × 4 = 240 miles

The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.

Therefore, the average speed on the level road was 60 miles per hour.