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Answer :
Final answer:
The rate of the faster bus is 134 km/h and the rate of the slower bus is 121 km/h.
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.
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