A cattle train left the station traveling east two hours before a diesel train.

Question

The diesel train traveled in the opposite direction going 15km/h slower than the cattle train for 9 hours after which time the trains were 1265km apart. What was the cattle train's speed?

Answer 1

The cattle train is going east the whole time, and the diesel train is going west.

We know the distance between the diesel train and cattle train after both have been traveling for 9 hours is 1265 kilometers. Writing d_diesel and d_cattle for the total diesel train and total cattle train distances, we can write equation 1:

1) d_diesel + d_cattle = 1265 km

The diesel train speed can be written as s_diesel and the cattle train speed can be written as s_cattle. We also know that distance = speed * time, which we will use throughout this problem.

We know that the diesel is 15 km/h slower, and is written as equation 2:

2) s_diesel = s_cattle - 15 km/h

What is the distance the diesel train traveled?

3) d_diesel = s_diesel * 9 hours = (s_cattle - 15 km/h) * 9 hours

where we plugged in equation 2.

But, don't forget the cattle train has been traveling for 11 hours! ( 9 hours + 2 hours). The cattle train distance in this 11 hours is:

4) d_cattle = s_cattle * 11 hours

Plug in equation 3 and equation 4 into equation 1 and solve for the speed of the cattle train, s_cattle:

5) (s_cattle - 15 km/h) * 9 hours + s_cattle * 11 hours = 1265 km

s_cattle * 9 hours - 135 km + s_cattle * 11 hours = 1265 km

s_cattle * ( 9 hours + 11 hours) =1400 km

s_cattle = 1400 km / 20 hours = 70 km/h