Speed if Travel 5.82 Miles in 97 Minutes
Distance-Rate-Fourth dimension 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 wait at a few other related products.
Distance = (Charge per unit)(Fourth dimension)
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 fourth dimension. On the CAHSEE test, you will be given ii of these and will exist asked to use the above equation to find the tertiary.
Example 1
It took Markus half an hour to drive home from work. He averaged 34 miles per 60 minutes. How far does Markus alive from his work?
Solution
Nosotros are given that it takes 1/2 an hour for the trip. This is a time:
t = 1/ii
We are given that he averages 34 miles per hour. This is a charge per unit:
r = 34
We are asked how few he has traveled. This is a distance. We apply the d=rt equation:
d = rt
= (34)(1/2)
= 17
Markus lives 17 miles from work.
Now try one by yourself. If y'all desire to see the answer, put your mouse on the yellow rectangle and the answer will appear.
Exercise 1
The electric current along the embankment is moving towards the south at ane.v miles per hour. If a piece of droppings is placed into the h2o, how far volition the current take information technology in half-dozen hours?
Example 2
Elena always rides her bike 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
Side by side, 24 miles is a distance. We accept:
d = 24
At present use the d=rt equation to go
24 = 15t
To solve this, split both sides by 15 to get
t = 24/15
Both are divisible by iii, and so this fraction reduces to
t = 8/5 = ane.half-dozen
Elena's ride takes 1.6 hours.
Now try 1 by yourself. If you want to see the answer, put your mouse on the xanthous rectangle and the answer will appear.
Exercise 2
Roberto will be driving from Los Angeles to Las Vegas tomorrow. He can boilerplate 60 miles per hr for the trip. Information technology is 282 miles from Los Angeles to Las Vegas. How long volition information technology take Roberto to bulldoze from Los Angeles to Las Vegas?
Example three
Juan has only completed a 5 kilometer race in xx minutes. What was his average speed in kilometers per 60 minutes?
Solution
First, 5 kilometers is a distance, so
d = five
Side by side, we are given xx minutes and we are asked to present the speed in kilometers per hr rather than kilometers per minute. We need to convert xx minutes to hours. Since there are lx minutes per 60 minutes, we dissever by 60 to notice out how many hours information technology took
t = xx minutes / 60 minutes per 60 minutes
= 1/3 hours
Now we can apply the d=rt equation:
5 = (r)(one/3)
If nosotros multiply both sides past 3, we get
(3)(v) = (r)(1/3)(3)
or
r = 15
Juan'south boilerplate speed was fifteen kilometers per 60 minutes.
Now try one by yourself. If you desire to see the answer, put your mouse on the yellow rectangle and the answer will announced.
Exercise iii
It takes 2 hours for a turtle to movement a altitude of 60 meters. How fast in kilometers per 60 minutes is the turtle moving?
Bug Involving Work
Related to the d=rt equation are problems that involve work. We volition expect at a few such examples.
Example 4
If one person paints the outside of a house, then information technology volition take that person 56 hours to complete the chore. If a team of 4 people each piece of work 7 hours per twenty-four hours, how many days will it take the team to paint the outside of the house?
Solution
The strategy that nosotros will take is to outset find out how many person-hours each twenty-four hour period the house is being painted. Since there are iv people on the chore and each works vii hours in a 24-hour interval, there are
(4)(7) = 28
person-hours each day. We can now dissever the number of hours to complete the job past the number of person-hours to observe the total number of days:
Days = (56 hours) / (28 person-hours per solar day)
= 2 days
It will take 2 days for the team to terminate painting the business firm.
Now try 1 past yourself. If you want to run across the answer, put your mouse on the yellow rectangle and the respond will announced.
Practise 4
It would take one person 72 hours to harvest the orange grove alone. If a three person team is hired for 8 hours per day per person, how many days will it take the team to harvest the orange grove?
Now for one more related example.
Case 5
A DVD burner can burn 12 DVDs per hour. A mill that has 150 DVD burners is in operation for 10 hours each day. How many DVDs will the factor burn per day?
Solution
Since i burner burns 12 DVDs per 60 minutes and there are 150 DVDs, we tin can multiply to find how many DVDs are burned in the factory:
Total DVDs per hour = (12)(150)
= 1800 DVDs per hr
Since the manufactory is in operation for 10 hours each day, we simply multiply by 10 to get the total number of DVDs burned per day:
DVDs per twenty-four hours = (1800 DVDs per 60 minutes)(10 hours per day)
= eighteen,000 DVDs per day
Now try i by yourself. If you desire to see the respond, put your mouse on the xanthous rectangle and the answer volition announced.
Exercise 5
Maria tin complete 32 arithmetic bug per minute. If she works a arithmetic issues for v minutes without stopping, how many arithmetics problems will she be able to complete?
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