A Man Usually Rides His Bike 9 Kilometers Per Hour
Distance-Charge per unit-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 charge per unit. We will as well wait at a few other related products.
Altitude = (Rate)(Time)
The equation that relates altitude, charge per unit, and time is
d = rt
Where d is the distance traveled, r is the rate, and t is the fourth dimension. On the CAHSEE exam, yous will be given two of these and will be asked to use the above equation to notice the third.
Example i
It took Markus half an hour to bulldoze home from piece of work. He averaged 34 miles per hr. 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 fourth dimension:
t = 1/two
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 utilize 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 yellowish rectangle and the answer will announced.
Exercise 1
The electric current along the embankment is moving towards the due south at i.5 miles per hour. If a piece of debris is placed into the water, how far will the current take it in 6 hours?
Example two
Elena ever rides her bicycle at a speed of 15 miles per hour. On Lord's day, she goes on a 24 mile bike ride. How many hours does this ride take?
Solution
The speed of xv miles per hour is a charge per unit. The fundamental words that tell us that this is a charge per unit are "speed" and "miles per hour". We can write:
r = 15
Side by side, 24 miles is a distance. We have:
d = 24
At present employ the d=rt equation to get
24 = 15t
To solve this, carve up both sides past 15 to get
t = 24/15
Both are divisible past 3, then this fraction reduces to
t = 8/v = i.vi
Elena'south ride takes 1.6 hours.
Now try i by yourself. If you lot want to see the answer, put your mouse on the yellow rectangle and the reply will appear.
Exercise ii
Roberto will be driving from Los Angeles to Las Vegas tomorrow. He can average 60 miles per hour for the trip. Information technology is 282 miles from Los Angeles to Las Vegas. How long volition it take Roberto to drive from Los Angeles to Las Vegas?
Example 3
Juan has just completed a 5 kilometer race in 20 minutes. What was his average speed in kilometers per 60 minutes?
Solution
Get-go, 5 kilometers is a distance, so
d = five
Adjacent, we are given twenty minutes and we are asked to present the speed in kilometers per hr rather than kilometers per minute. We need to convert 20 minutes to hours. Since at that place are sixty minutes per hour, we divide by 60 to find out how many hours it took
t = xx minutes / threescore minutes per hour
= one/3 hours
Now we can utilize the d=rt equation:
5 = (r)(1/3)
If nosotros multiply both sides past 3, we get
(3)(5) = (r)(1/3)(3)
or
r = xv
Juan's average speed was 15 kilometers per hour.
Now endeavour one by yourself. If you desire to see the answer, put your mouse on the yellow rectangle and the answer will announced.
Exercise 3
It takes ii hours for a turtle to move a distance of threescore meters. How fast in kilometers per 60 minutes is the turtle moving?
Problems Involving Piece of work
Related to the d=rt equation are problems that involve work. We volition look at a few such examples.
Example four
If one person paints the outside of a house, so it volition take that person 56 hours to consummate the job. If a team of 4 people each work 7 hours per solar day, how many days volition information technology take the team to paint the exterior of the house?
Solution
The strategy that we will accept is to first find out how many person-hours each mean solar day the house is being painted. Since there are 4 people on the job and each works 7 hours in a 24-hour interval, there are
(4)(seven) = 28
person-hours each day. We can now carve up the number of hours to complete the task by the number of person-hours to notice 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 cease painting the house.
At present try one past yourself. If you want to run into the answer, put your mouse on the yellow rectangle and the answer volition appear.
Exercise four
It would take ane person 72 hours to harvest the orange grove lonely. If a iii person team is hired for 8 hours per day per person, how many days volition it take the squad to harvest the orange grove?
Now for one more related example.
Case five
A DVD burner can burn 12 DVDs per hour. A manufactory that has 150 DVD burners is in operation for 10 hours each twenty-four hours. How many DVDs volition the factor fire per mean solar day?
Solution
Since one burner burns 12 DVDs per hour and in that location are 150 DVDs, nosotros tin multiply to find how many DVDs are burned in the factory:
Full DVDs per hr = (12)(150)
= 1800 DVDs per hr
Since the factory is in operation for 10 hours each day, we just multiply by x to get the total number of DVDs burned per day:
DVDs per day = (1800 DVDs per hr)(x hours per day)
= xviii,000 DVDs per day
Now attempt ane past yourself. If you want to see the reply, put your mouse on the xanthous rectangle and the answer will appear.
Exercise five
Maria tin complete 32 arithmetic bug per minute. If she works a arithmetic problems for 5 minutes without stopping, how many arithmetic issues will she be able to consummate?
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Source: https://ltcconline.net/greenl/courses/CAHSEE/Geometry/drt.htm
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