Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 mi/h slower than the other. If the two buses are 276 miles apart after 2 hours, what is the rate of each bus?

Note that the ALEKS graphing calculator can be used to make computations easier.
Rate of the slower bus: ____ mi / h
Rate of the faster bus: _____ mi / h

Answer 1

• slower: 64 mi/h
• faster: 74 mi/h

Explanation:

You want to know the individual speeds of two buses traveling in opposite directions such that they are 276 miles apart after 2 hours, and one is 10 mph faster.

Setup

The rate of separation is the sum of their speeds. That rate is the distance divided by the time:

separation speed = separation distance / time

x + y = 276/2 . . . . . miles per hour

The difference of speeds can be represented by ...

x - y = 10

Solution

A graph of these two equations shows a point of intersection at (x, y) = (74, 64).

The faster bus is traveling at 74 miles per hour; the slower bus is traveling at 64 miles per hour.