Train a and train b

Question

The speed of train A is 6 mph slower than the speed of B. Train A travels 230 miles in same time it takes train B to travel 260 miles. Find the speed of each train.

Answer 1

Distance = rate x time or D = rt. This can be resolved for time as t = D/r.

 

If x= speed of train B, then the time it take to travel the distance 260 miles would be 260/x

 

The speed of train A would be x - 6 since it is 6 mph slower.  The time to travel the distance 230 miles would be 230/(x - 6).

 

If we set them equal to each other since the times are equal:

 

260/x = 230/(x-6)

 

Cross multiply to solve:

 

230x = 260(x-6)

230x = 260x - 1560

-30x = -1560

x= 52 mph (Train B's speed.)

 

Train A is going 6 mph slower, so it's speed is 46 mph.