Question

7.66. 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. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass on the highway (not in the station)?

Answer 1

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.

Answer 2

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