ramon drives at an average speed of 35 kph on a journey of 140 km. How long does the journey take?
Answers
Explanation:
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.
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 2
Roberto will be driving from Los Angeles to Las Vegas tomorrow. He can average 60 miles per hour for the trip. It is 282 miles from Los Angeles to Las Vegas. How long will it take Roberto to drive from Los Angeles to Las Vegas?
4.7 hours
Example 3
Juan has just completed a 5 kilometer race in 20 minutes. What was his average speed in kilometers per hour?
Solution
First, 5 kilometers is a distance, so
d = 5
Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute. We need to convert 20 minutes to hours. Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took
t = 20 minutes / 60 minutes per hour
= 1/3 hours
Now we can use the d=rt equation:
5 = (r)(1/3)
If we multiply both sides by 3, we get
(3)(5) = (r)(1/3)(3)
or
r = 15
Juan's average speed was 15 kilometers per hour.
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 3
It takes 2 hours for a turtle to move a distance of 60 meters. How fast in kilometers per hour is the turtle moving?