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Answer :
The slower bus travels at 114 km/h, whereas the faster bus travels at
[tex]\(114 + 13 = 127\)[/tex] km/h.
Let's denote the rate of the slower bus as [tex]\(x\)[/tex] km/h. Since the other bus travels 13 km/h faster, the rate of the faster bus can be expressed as [tex]\(x + 13\)[/tex] km/h.
To find the rates of each bus, we can use the formula:
[tex]\[ \text{rate} = \frac{\text{distance}}{\text{time}} \][/tex]
The slower bus travels for 5 hours at rate [tex]\(x\)[/tex] km/h, so its distance covered is [tex]\(5x\)[/tex] km. Similarly, the faster bus travels for 5 hours at rate[tex]\(x + 13\)[/tex] km/h, so its distance covered is [tex]\(5(x + 13)\)[/tex] km.
Since they are traveling towards each other, the sum of the distances covered by each bus must equal the total distance between the towns, which is 1205 km.
[tex]\[ 5x + 5(x + 13) = 1205 \][/tex]
Simplifying the equation:
[tex]\[ 5x + 5x + 65 = 1205 \]\[ 10x = 1140 \]\[ x = 114 \][/tex]
Therefore, the rate of the slower bus is 114 km/h, and the rate of the faster bus is [tex]\(114 + 13 = 127\)[/tex] km/h.
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