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 2 hours. Find the average speed on the level road if the entire trip was 266 miles.

Answer 1

To find the average speed on the level road, an equation relating the total distance of the trip and the speed difference on different road types was used. The total trip was 266 miles, and by setting up the equation and solving for the average speed, it was determined to be 51 miles per hour.

Step-by-step explanation:

To find the average speed on the level road for the bus's trip, we need to establish an equation that relates the distances on the level road and winding road with their respective average speeds and times.

Let's call the average speed on the level road v. Since the bus was moving 20 miles per hour slower on the winding road, the average speed there would be v - 20 miles per hour. We were given that the time spent on the level road was 4 hours and on the winding road it was 2 hours.

The total distance covered by the bus on the level road is distance = speed × time, which in this case would be v × 4. Similarly, the distance covered on the winding road is (v - 20) × 2.

Since the entire trip was 266 miles, we can set up this equation:

v × 4 + (v - 20) × 2 = 266

Solving for v will give us the average speed on the level road:

4v + 2v - 40 = 266

6v = 306

v = 51

Therefore, the average speed on the level road was 51 miles per hour.