Question

Two buses leave towns 1020 kilometers apart at the same time and travel toward each other. one bus travels 13 km/h slower than the other. if they meet in 4 hours, what is the rate of each bus?

Answer 1

The rate of the faster bus is 134 km/h and the rate of the slower bus is 121 km/h.

Step-by-step explanation:

Let's represent the rate of the faster bus as 'x' km/h. Since the other bus is traveling 13 km/h slower, its rate can be represented as 'x - 13' km/h.

When two buses travel towards each other, the sum of their distances covered is equal to the total distance between them.

In this case, the total distance between the towns is 1020 km. So, after 4 hours, the sum of the distances covered by both buses would be 1020 km.

Using the formula:

Distance = Rate * Time

We can set up the equation:

x * 4 + (x - 13) * 4 = 1020

Simplifying the equation, we get:

4x + 4x - 52 = 1020

Combining like terms, we get:

8x - 52 = 1020

Adding 52 to both sides:

8x = 1072

Dividing both sides by 8:

x = 134

So, the rate of the faster bus is 134 km/h and the rate of the slower bus is 134 - 13 = 121 km/h.