Intro to Algebra help

Question

A bus traveled on a level road for 6 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 6 hours. Find the average speed on the level road if the entire trip was 672 miles.

Answer 1

Let's start by breaking down the information given to us in the problem:

1) There are two sections of road that add up to 672 miles.

2) On both sections of road, the bus traveled for 6 hours, adding up to a total time of 12 hours.

3) The bus drove at an average speed 20 mph faster than it traveled on the winding road.

We can relate distance, time, and velocity, by the equation: d = v*t, which states that the total distance an object traveled is equal to its average velocity multiplied by the total time it traveled. Let's assume for this question that average velocity is equal to average speed.

We are given the distance the bus travels, which is equal to 672 miles. The average speed, however, is not constant for that entire distance. The bus travels faster on the level road than on the winding road. We can express the average speed that the bus travels on the level road as v, and the average speed the bus travels on the winding road as (v - 20).

The v*t term in the above equation can be broken up into different pieces, given that the average speed of the bus changed during the trip. We can rewrite the above equation as:

672 = (v)*6 + (v - 20)*6

Which states that the total distance traveled (672 miles) is equal to the average velocity on the level road (v) times the total time on that road (6 hours) plus the average velocity on the winding road (v - 20) times the total time on that road (6 hours).

We can solve this equation for v as follows:

672 = v*6 + (v - 20)*6 => 112 = v + v - 20 => 132 = 2*v => v = 66

So we have found the average speed of the bus on the level road to be 66 mph.

Hope this helps!