Question

A bus traveled on a level road for 6 hours at an average speed 20mph faster that it traveled on a winding road. The time spent on the winding road was 2 hours. Find the average speed on the level road is the entire trip was 504 miles.

Answer 1

To find the average speed on the level road, we first define the speed on the winding road as 'x' mph. Using the equation 6(x + 20) + 2x = 504, we solve for 'x' to find that the average speed on the winding road is 48 mph. Therefore, the average speed on the level road is 68 mph.

Step-by-step explanation:

The question involves using algebraic methods to determine the average speed on a level road for a bus that traveled a total of 504 miles with part of the journey on a winding road. To solve this, we can use the relationship that distance equals speed times time (d = vt).

Step-by-Step Explanation

Let's define the average speed on the winding road as 'x' mph. Therefore, the average speed on the level road would be 'x + 20' mph. We know the bus spent 6 hours on the level road and 2 hours on the winding road. Using the d = vt formula:

• The distance covered on the level road is 6(x + 20)miles.
• The distance covered on the winding road is 2x miles.

As the total distance is 504 miles, the equation to find 'x' is:

6(x + 20) + 2x = 504

Solve this equation:

6x + 120 + 2x = 504

8x + 120 = 504

8x = 504 - 120

8x = 384

x = 384 / 8

x = 48 mph (speed on winding road)

Therefore, the speed on the level road is:

x + 20 = 48 + 20 = 68 mph

The average speed on the level road is 68 mph.