Thread: word problem...help please...

A car leaves town A in the direction of town B. An hour later a motorcycle leaves town A in the direction of town B at 75 km/h. The motorcycle reached the car and returned to town A. The car arrived at town B, at the same time that the motorcycle returned to town A.
The Distance between the towns is 250 km.
Find the car's speed.

Originally Posted by balmora55

A car leaves town A in the direction of town B. An hour later a motorcycle leaves town A in the direction of town B at 75 km/h. The motorcycle reached the car and returned to town A. The car arrived at town B, at the same time that the motorcycle returned to town A.
The Distance between the towns is 250 km.
Find the car's speed.

Okay, I found this solution by guess and check, but will try to devise a method. For the time being I'll explain how I checked. The car should be traveling at 50 km/h. I found this by starting:

Point A is at 0 km and Point B is at 250 km.

Hour 1 elapses:
Motorcycle at 0 km
Car at 50 km

Hour 2 elapses:
Motorcycle at 75 km
Car at 100 km

Hour 3 elapses: This is the point at which they meet and the motorcycle turns around.
Motorcycle at 150 km
Car at 150 km

Hour 4 elapses:
Motorcycle at 75 km (travelling back to point A)
Car at 200 km

Hour 5 elapses:
Motorcycle at 0 km (Point A)
Car at 250 km (Point B)