Answer :
Final answer:
In a problem involving two buses traveling towards each other from towns 945km apart, with one bus 13km/h slower than the other and meeting after 5 hours, the rates of the buses are found to be 105km/h and 92km/h respectively.
Explanation:
The subject of this question falls under the Mathematics field, specifically within the topic of rate problems. Let's establish that the faster bus is traveling at 'r' km/h, which makes the slower one travel at 'r-13' km/h. Because they travel for the same amount of time and towards each other, we know that the sum of their traveled distances will add up to the total distance between the towns.
So, we can express this situation with the equation 5r + 5(r - 13) = 945. Solving this equation, we find r = 105 km/h, meaning the speed of the faster bus is 105 km/h, and the slower bus travels at 105 - 13 = 92 km/h. Thus, these are the rates of each bus.
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