Distance Word Problems - Free Printable

Let $x$ be the number of hours the freight train traveled before the diesel train caught up.

Since the diesel train left one hour later, it traveled for $x - 1$ hours when it caught up.

The distance traveled by the freight train is $28x$ miles.

The distance traveled by the diesel train is $33(x - 1)$ miles.

When the diesel train catches up, both trains have traveled the same distance:

$$
28x = 33(x - 1)
$$

Solve for $x$:

$$
28x = 33x - 33
$$

$$
28x - 33x = -33
$$

$$
-5x = -33
$$

$$
x = \frac{33}{5} = 6.6
$$

The freight train traveled for 6.6 hours before the diesel train caught up.