There are many real-world situations in which something keeps happening at the same rate. In these situations, we can use equivalent ratios or unit rates to make predictions or to answer questions about the quantities.

For example, the school cafeteria serves 600 students in 40 minutes. At this rate, how long will it take the cafeteria to serve 750 students?

We can use a table or a double number line diagram to find ratios that are equivalent to the given ratio.

Both the double number line diagram and table show that it will take the cafeteria 50 minutes to serve 750 students.

Double number line, 4 evenly spaced tick marks. Top line, number of students. Beginning at first tick mark, labels: 0, 150, 300, 450, 600, 750, 900. Bottom line, time in minutes. Beginning at first tick mark, labels: 0, 10, 20, 30, 40, 50, 60. 

How many students can the cafeteria serve in 27 minutes?

In this case, it is helpful to find a unit rate—the number of students the cafeteria can serve per minute. Dividing the number of students, 600, by the number of minutes, 40, gives us this unit rate.   , so the cafeteria can serve 15 students per minute. This means that in 27 minutes it can serve , or 405 students.