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
Rates and speeds are common on GMAT problem-solving problems. One of the ways the test-makers can make such problems more challenging is by switching between units of measurement. Learn a quick and easy way to keep track of rate conversions in this video, and outsmart the GMAT!