Answer:
Assuming the buses travel on the same highway, the number of Dallas-bound buses does a Houston-bound bus pass on the highway is 10 buses.
Step-by-step explanation:
Given:
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half-hour.
The trip from one city to the other takes 5 hours.
Find:
Assuming the buses travel on the same highway, the number of Dallas-bound buses does a Houston-bound bus pass on the highway (not in the station)
Step 1 of 1
We count the number of Dallas-bound buses that a single Houston-bound bus passes.
There are two groups of Dallas-bound buses that we have to consider.
First, there are the buses that were on the way to Dallas at the time the Houston-bound bus leaves Dallas.
Second, there are the buses that leave Houston after the Houston-bound bus starts but before it arrives at Houston.
In order for a bus to be on the way to Dallas when the Houston-bound bus leaves, it must have left Houston less than 5 hours before the Houston-bound bus leaves.
There is one such bus each hour, for a total of 5 buses.
In order for a Dallas-bound bus to leave Houston after the Houston-bound bus leaves but before the Houston-bound bus arrives, the Dallas-bound must leave Houston within 5 hours after the Houston-bound bus leaves.
Again, there is one such bus each hour, for a total of 5 more buses than the Houston-bound bus passes.
Therefore, the Houston-bound bus passes 5+5=10 Dallas-bound buses.
