Question

Two busses are traveling in opposite directions. After 5 hours they are 400 miles apart. If the faster bus travels 3 times as fast as the slower bus, how fast does the faster bus travel?

Answer 1

The speed of the faster bus is 60 miles per hour, calculated by determining the relative speed and solving the equation for the given ratio of speeds.

Step-by-step explanation:

To solve the problem of determining the speed of the faster bus when two buses are traveling in opposite directions, we can use the concept of relative speed. Since the buses are moving apart, we add their speeds together to get the relative speed, which is the rate at which the distance between them increases. After 5 hours they are 400 miles apart, so their relative speed is ​​400 miles / 5 hours = 80 miles per hour.

Let's denote the speed of the slower bus as 'x' miles per hour. Therefore, the speed of the faster bus will be '3x' miles per hour. The sum of their speeds equals the relative speed: x + 3x = 80. Solving for x gives us that x = 20 miles per hour. Hence, the faster bus travels at 3x = 3 * 20 = 60 miles per hour.