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Distance-Rate-Time Applications. Example 1:. Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If t he rate on the ride home was 20mph faster than the rate going to w ork, what is the distance from her home to work?. - PowerPoint PPT Presentation
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Distance-Rate-Time Applications
Example 1:
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the rate on the ride home was 20mph faster than the rate going to work, what is the distance from her home to work?
1) Variable declaration:
Distance-Rate-Time Applications
Example 1:
1) Variable declaration:
Since the rate going home is in terms of the rate going to work, let x represent the rate going to work.
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the rate on the ride home was 20mph faster than the rate going to work, what is the distance from her home to work?
D r t
To Work
Return Home
The rate returning home was 20mph faster than the rate going, or x+20.
x20x
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the rate on the ride home was 20mph faster than the rate going to work, what is the distance from her home to work?
D r t
To Work
Return Home
The time going to work is 30 minutes, or …
x
30min1 hour
60min
2
1 hour
2
1/220x
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the rate on the ride home was 20mph faster than the rate going to work, what is the distance from her home to work?
D r t
To Work
Return Home
The time returning home is 10 minutes, or …
x
10min1 hour
60min
6
1 hour
6
1/21 / 6
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the rate on the ride home was 20mph faster than the rate going to work, what is the distance from her home to work?
20x
D r t
To Work
Return Home
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the ride home was 3 times the rate going to work, what is the distance from her home to work?
Since distance = rate × time, the distance to work is the product of the rate and time …
x 1/21 / 6
1/2 x
Do the same with the distance home …
1/6 20x 20x
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the ride home was 3 times the rate going to work, what is the distance from her home to work?
Since the distances are the same, we have …
12x 1
206x
2) Write the equation
D r t
To Work
Return Home
x 1/21 / 6
1/2 x 1/6 20x 20x
3) Solve the equation:
1 120
2 6x x
6 63
3 20x x
2 20x
10x
4) Write an answer in words, explaining the meaning in light of the application
What was asked for in the application
Amy rides her bike to work in 30 minutes. On the way home she catches a ride with a friend and arrives home in 10 minutes. If the ride home was 3 times the rate going to work, what is the distance from her home to work?
x = rate riding to work
The rate riding to work was 10 mph.
10x
1/2 hour = time riding to work
The distance from home to work was 5 miles.
d r t
110
2
5
Distance-Rate-Time Applications
Example 2:
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
1) Variable declaration:
Distance-Rate-Time Applications
Example 2:
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
Since Sam’s rate is given in terms of Mary’s rate, let x represent Mary’s rate.
1) Variable declaration:
D r t
Sam
Mary
Sam’s rate is 10 mph slower than Mary’s, or x-10.
x10x
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
D r t
Sam
Mary
Both Sam and Mary were traveling the same amount of time, from 11:00am to 3:00pm, which is 4 hours.
x10x
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
44
D r t
Sam
Mary x10x
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
44
Since distance = rate × time, Sam’s distance is …
… and Mary’s distance is…
4 10x4x
D r t
Sam
Mary x10x
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
44
4 10x4x
(Sam’s distance) + (Mary’s distance) = 480 miles
4 10x
2) Write the equation
4x 480
3) Solve the equation:
4 10 4 480x x
4 40 4 480x x
8 40 480x
8 520x
65x
4) Write an answer in words, explaining the meaning in light of the application
What was asked for in the application
Max leaves a gas station in Denver at 11:00am heading west. At the same time, Mary leaves the same station heading east. Since Max is driving in the mountains, his average rate is 10 mph slower than Mary’s. At 3:00pm they are 480 miles apart. Determine Max’s rate.
x =Mary’s rate
Mary’s rate was 65 mph.
65x
Max’s rate was x – 10.
Max’s rate was 55 mph.
10 65 10x
55
Distance-Rate-Time Applications
Example 3:
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
1) Variable declaration:
Let x represent the rate of the plane in still air.
D r t
Against the wind
With the wind
When the plane is going against the wind, the ground speed is reduced by the rate of the wind.
30x
The rate against the wind is given by …
(rate of the plane) - (rate of the wind)
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
D r t
Against the wind
With the wind
When the plane is going with the wind, the ground speed is increased by the rate of the wind.
30x
The rate with the wind is given by …
(rate of the plane) + (rate of the wind)
30x
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
D r t
Against the wind
With the wind
The time against the wind is 3 hours …
30x
… and the time with the wind is 2 hours.
30x
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
32
D r t
Against the wind
With the wind30x 30x
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
32
Since distance = rate × time, the distance against the wind is …
… and the time with the wind is…
3 30x 2 30x
D r t
Against the wind
With the wind30x 30x
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
32
3 30x 2 30x
3 30x
2) Write the equation
2 30x 1270
(distance against the wind)+(distance with the wind) = 1270
3) Solve the equation:
3 30 2( 30) 1270x x
3 90 2 60 1270x x 5 30 1270x
5 1300x 260x
4) Write an answer in words, explaining the meaning in light of the application
What was asked for in the application
A plane travels against a 30mph wind for 3 hours. Then the plane travels with the same wind for 2 hours. The combined distance is 1270 miles. Determine the rate of the plane in still air.
x = rate of the plane
The plane’s rate in still air was 260 mph.
260x
