A salesman made a trip of 420 miles by bus and train. He traveled 3 hours by bus and 5 hours by train. If the train averaged 12 mph more than the bus, find the rate of each.

The speed at which the buss made the trip was 45 mph and the train was 57 mph.

Step-by-step explanation:

The average speed is given by:

speed = distance / time

Therefore we can manipulate it to give us the distance:

distance = speed*time

The time distance of each stage of his trip summed must be equal to the total distance of the trip. Since he made a trip in two legs, one by bus that lasted 3 h at a speed of "x" and one that lasted 5 hours at a speed of "x + 12". We have:

420 = 3*x + 5 * (x + 12)

3*x + 5 * (x + 12) = 420

3*x + 5*x + 60 = 420

8*x = 420 - 60

8*x = 360

x = 45 mph

The speed at which the buss made the trip was 45 mph and the train was 57 mph.