The distance *d* that an object will travel is equal to its rate *r* times its time *t*.

*d* = *r t*

Rate is sometimes called speed or velocity. Rates are given as ratios, such as “miles per hour” or mph and “kilometers per hour” or km/h.

The distance covered in 1 hour at 20 miles per hour is the same as the distance covered in 30 minutes at 40 miles per hour.

*d* = *r t*, so 20 mph × 1 hour = 40 mph × 30 minutes

When setting up an equation, make sure that the units match. The rates 1 mile per minute and 60 miles per hour are the same.

1 mile/1 minute × 60 minutes/1 hour = 60 miles/1 hour

The most common methods for solving motion problems are to use a system of equations or to use a proportion.

**Converting Rates and Speeds**