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Truck and Car. Given the rates of two vehicles approaching each other, the student will be able to find the time at which they meet by using the formula D=RT. California State Standard 15.0: Students apply algebraic techniques to solve rate problems. A. B. Truck and Car. - PowerPoint PPT Presentation
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Truck and Car
Given the rates of two vehicles approaching each other, the
student will be able to find the time at which they meet by using
the formula D=RT.
California State Standard 15.0: Students apply algebraic techniques
to solve rate problems.
Truck and Car
Towns A and B are 300 miles apart. At noon, a truck leaves town A toward town B, and the car leaves town B toward town A. The car drives at 70 mph and the truck drives at 80 mph. When and where do they meet? First, let’s try to solve the problem by drawing a picture.
A B
Vocabulary
• Distance: how far away one thing is from another.
• Rate: speed, or how fast something is going.
A B
Thinking About the Problem
1. How long do you think it would take the Truck to get from one town to the other?
2. How did you decide that?
3. How long would it take the car to get from one town to the next?
4. Do you think they will meet half way between?
5. Why or why not?
Position of Each Vehicle After 1 Hour
80 miles 70 miles
A B
Position of Each Vehicle After 2 Hours
160 miles 140 miles
A B
Solving the Problem by Using a Table
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour
1 Hour
1 ½ Hour
2 Hours
Solving the Problem by Using a Table
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles 35 Miles 75 Miles
1 Hour
1 ½ Hour
2 Hours
Solving the Problem by Using a Table
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles 35 Miles 75 Miles
1 Hour 80 Miles 70 Miles 150 Miles
1 ½ Hour
2 Hours
Solving the Problem by Using a Table
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles 35 Miles 75 Miles
1 Hour 80 Miles 70 Miles 150 Miles
1 ½ Hour 120 Miles 105 Miles 225 Miles
2 Hours
Solving the Problem by Using a Table
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles 35 Miles 75 Miles
1 Hour 80 Miles 70 Miles 150 Miles
1 ½ Hour 120 Miles 105 Miles 225 Miles
2 Hours 160 Miles 140 Miles 300 Miles
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles
80 (0.5)
35 Miles
70 (0.5)
75 Miles
1 Hour 80 Miles 70 Miles 150 Miles
1 ½ Hour 120 Miles 105 Miles 225 Miles
2 Hours 160 Miles 140 Miles 300 Miles
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles
80 (0.5)
35 Miles
70 (0.5)
75 Miles
1 Hour 80 Miles
80 (1)
70 Miles
70 (1)
150 Miles
1 ½ Hour 120 Miles
80 (1.5)
105 Miles
70 (1.5)
225 Miles
2 Hours 160 Miles
80 (2)
140 Miles
70 (2)
300 Miles
Time Distance Truck Drove
Distance Car Drove
Total Distance
½ Hour 40 Miles
80 (0.5)
35 Miles
70 (0.5) 75 Miles
1 Hour 80 Miles
80 (1)
70 Miles
70 (1) 150 Miles
1 ½ Hour 120 Miles
80 (1.5)
105 Miles
70 (1.5) 225 Miles
2 Hours 160 Miles
80 (2)
140 Miles
70 (2) 300 Miles
Rate (Time) + Rate (Time) = Total Distance
+ =
+ =
+ =
+ =
What do you notice about the times?
Rate (Time) + Rate (Time) = Total Distance
Rate (Time) + Rate (Time) = Total Distance
80(T) + 70(T) = 300 miles
What do you notice about the times?
Rate (Time) + Rate (Time) = Total Distance
Rate (Time) + Rate (Time) = Total Distance
80(T) + 70(T) = 300 miles
150(T) = 300 miles
150 150 2 Hours
• A cheetah and a jaguar are 600 meters apart. They begin to run toward a gazelle at the same time. The cheetah begins at the rock running 30 meters per second, and the jaguar begins at the tree running 20 meters per second. If they get to the gazelle at the same time, where is the gazelle located? How long did it take them to get there?
600 meters
Fin
