The average speed on a city street is 35 miles per hour (mph). Assuming you drive the speed limit, how long will it take you to
drive 7 miles? Use the formula d=rt.

Distance-Rate-Time and other Products

In this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate. We will also look at a few other related products.

Distance = (Rate)(Time)

The equation that relates distance, rate, and time is

d = rt

Where d is the distance traveled, r is the rate, and t is the time. On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find the third.

Example 1

It took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?

Solution

We are given that it takes 1/2 an hour for the trip. This is a time:

t = 1/2

We are given that he averages 34 miles per hour. This is a rate:

r = 34

We are asked how few he has traveled. This is a distance. We use the d=rt equation:

d = rt

= (34)(1/2)

= 17

Markus lives 17 miles from work.

Now try one by yourself. If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.

Exercise 1

The current along the beach is moving towards the south at 1.5 miles per hour. If a piece of debris is placed into the water, how far will the current take it in 6 hours?

9 miles

Example 2

Elena always rides her bicycle at a speed of 15 miles per hour. On Sunday, she goes on a 24 mile bike ride. How many hours does this ride take?

Solution

The speed of 15 miles per hour is a rate. The key words that tell us that this is a rate are "speed" and "miles per hour". We can write:

r = 15

Next, 24 miles is a distance. We have:

d = 24

Now use the d=rt equation to get

24 = 15t

To solve this, divide both sides by 15 to get

t = 24/15

Both are divisible by 3, so this fraction reduces to

t = 8/5 = 1.6

Elena's ride takes 1.6 hours.