Final answer:
The speed of the slower bus is 15 mph, the speed of the faster bus is 25 mph, and the distance between towns A and B is 87.5 miles. This was determined by setting up equations based on the speed and time taken by each bus and solving for the speeds and distance.
Step-by-step explanation:
We have two buses traveling from town A to town B, with one bus traveling 10 mph faster than the other. Let v be the speed of the slower bus, then the speed of the faster bus would be v + 10 mph. The faster bus travels for 3.5 hours to reach town B, and thus covers a distance of (v + 10) * 3.5 miles.
The slower bus still has 1/6 of the distance to travel after 3.5 hours. Hence, it has covered 5/6 of the distance between towns A and B, which is equal to 5/6 * (v * 3.5) miles. Since both buses cover the same distance, we can equate the two expressions and solve for v:
(v + 10) * 3.5 = (5/6) * (v * 3.5).
Solving this equation:
- 3.5v + 35 = (35/6)v.
- Multiplying by 6 to clear the fraction: 21v + 210 = 35v.
- Subtracting 21v from both sides: 210 = 14v.
- Dividing by 14: v = 15 mph.
Therefore, the speed of the slower bus is 15 mph and the speed of the faster bus is 25 mph (15 mph + 10 mph).
To find the distance between towns A and B, we use the speed of the faster bus:
- Distance = speed × time,
- Distance = 25 mph × 3.5 hours,
- Distance = 87.5 miles.
Hence, the distance between towns A and B is 87.5 miles.