Diego ran 3 kilometers in 20 minutes. Andre ran 2,550 meters in 17 minutes. Who ran faster? Since neither their distances nor their times are the same, we have two possible strategies:

• Find the time each person took to travel the same distance. The person who traveled that distance in less time is faster.

• Find the distance each person traveled in the same time. The person who traveled a longer distance in the same amount of time is faster.

It is often helpful to compare distances traveled in 1 unit of time (1 minute, for example), which means finding the speed, such as meters per minute.

Let’s compare Diego and Andre’s speeds in meters per minute.

A table with two columns. First column, distance in meters, 3000, 1500, 150. Second column, time in minutes, 20, 10, 1. Outside the table, arrows between first and second row say "times one-half." Arrows between second and third row say "times one-tenth." 

A table with two columns. First column, distance in meters, 2550, 150. Second column, time in minutes, 17, 1. Outside the table, arrows between first and second row say "times one-seventeenth."

Both Diego and Andre ran 150 meters per minute, so they ran at the same speed.

Finding ratios that tell us how much of quantity per 1 unit of quantity is an efficient way to compare rates in different situations. Here are some familiar examples:

• Car speeds in miles per hour.

• Fruit and vegetable prices in dollars per pound.