Question

A diesel train left Washington and traveled

toward Johannesburg at an average speed of
52 mph. A cattle train left two hours later
and traveled in the same direction but with
an average speed of 60 mph. Find the
number of hours the diesel train traveled
before the cattle train caught up.

Answer 1

The number of hours the diesel train traveled before the cattle train caught up is 15 hours

Solution:

Let t = travel time of the diesel train

Then (t - 2) is the travel time of the cattle train (Left 2 hrs later)

Average speed of diesel train = 52 mph

Average speed of cattle train = 60 mph

To find: number of hours the diesel train traveled before the cattle train caught up

Distance = speed x time

Distance traveled by diesel train:

Distance = 52 x t = 52t

Distance traveled by cattle train:

Distance = 60 x (t - 2) = 60t - 120

When the cattle train catches the diesel, they will have traveled the

same distance

Distance traveled by diesel train = Distance traveled by cattle train

52t = 60t - 120

60t - 52t = 120

8t = 120

t = 15

Thus the number of hours the diesel train traveled before the cattle train caught up is 15 hours