Answer :
Final answer:
To determine the rate of each bus heading towards each other from 339 miles apart, we set up an equation using their speeds and the fact that they meet after 3 hours. The faster bus travels at 63 mph and the slower one at 50 mph.
Explanation:
When two buses are traveling towards each other from towns 339 miles apart and meet after 3 hours, to find the rate of each bus, we can set up an equation based on the relative speeds and the distance traveled. Let's denote the speed of the faster bus as v mph. Consequently, the slower bus travels at v - 13 mph. Since they meet after 3 hours, we know that the sum of the distances they travel is equal to 339 miles.
So we have:
- v (speed of the faster bus)
- v - 13 (speed of the slower bus)
Distance = Speed
Time, so:
(v
3) + ((v - 13)
3) = 339
Solving the equation:
3v + 3(v - 13) = 339
3v + 3v - 39 = 339
6v = 378
v = 63
So, the faster bus travels at 63 mph, and the slower bus travels at 50 mph.