Find the diesel train's speed.

Question

A diesel train left Miami traveling north
3.6 hours before a cattle train. The cattle
train traveled in the opposite direction
going 22 mph slower then the diesel train
for 8.5 hours after which time the trains
were 1461 mi. apart. 

Answer 1

Remember that distance = rate × time. We'll write two equations: one for the diesel train and one for the cattle train.

 

 

 

DIESEL TRAIN

 

We're not told how far the diesel train traveled, so call the distance d. We're not sure how fast the diesel train traveled, so call the rate r. The diesel train traveled for 3.6 hours and then an additional 8.5 hours, so time = 3.6 + 8.5 = 12.1. So:

 

d = 21.1r

 

 

 

CATTLE TRAIN

 

We're not told how far the cattle train traveled, but since the trains traveled a combined 1461 miles, we can call the distance 1461 - d. We're not told how fast the cattle train traveled, but we know it was 22 mph slower than the diesel train, so call the rate r - 22. The cattle train traveled for 8.5 hours. So:

 

1461 - d = 8.5(r - 22)

 

 

 

Now you have a system of equations:

 

d = 12.1r

1461 - d = 8.5(r - 22)

 

Solve the second equation for d, then substitute that into the first equation to solve for r:

 

1461 = d + 8.5(r - 22)

1461 - 8.5(r - 22) = d

 

d = 12.1r

1461 - 8.5(r - 22) = 12.1r

1461 - 8.5r + 187 = 12.1r

1648 - 8.5r = 12.1r

1648 = 20.6r

80 = r

 

The diesel train traveled at a rate (speed) of 80 MPH.