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Answer :
Final answer:
The speed of the slower bus is 71 miles per hour and the speed of the faster bus is 84 miles per hour. The total 465 miles is calculated by adding the distances covered by both buses in 3 hours.
Explanation:
To solve the problem involving two buses traveling in opposite directions, we use the concept that distance is the product of speed and time. In this case, the two buses are moving apart, so we add their speeds to find the combined rate at which the distance between them increases. Let x be the speed of the slower bus in miles per hour. Since the faster bus travels 13 mi/h faster, its speed would be x + 13 mi/h. The buses travel for 3 hours and are 465 miles apart after this time. The total distance covered by the two buses in 3 hours is 3x (from the slower bus) + 3(x + 13) (from the faster bus), which equals 465 miles. So the equation we use to find the speeds is 3x + 3(x + 13) = 465. By solving this equation: 3x + 3x + 39 = 465, 6x = 465 - 39, 6x = 426, x = 71. So, the speed of the slower bus is 71 mi/h, and the speed of the faster bus is 71 + 13 = 84 mi/h. Both buses contribute to the total distance as they travel in opposite directions. The sum of their speeds gives us the rate at which this total distance increases over time.
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