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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.

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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, lets try to solve the problem by drawing a picture. AB

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Vocabulary Distance: how far away one thing is from another. Rate: speed, or how fast something is going. AB

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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?

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Position of Each Vehicle After 1 Hour AB

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80 miles 70 miles AB

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Position of Each Vehicle After 1 Hour AB

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Position of Each Vehicle After 2 Hours 160 miles 140 miles AB

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Solving the Problem by Using a Table TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour 1 Hour 1 ½ Hour 2 Hours

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Solving the Problem by Using a Table TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles35 Miles75 Miles 1 Hour 1 ½ Hour 2 Hours

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Solving the Problem by Using a Table TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles35 Miles75 Miles 1 Hour80 Miles70 Miles150 Miles 1 ½ Hour 2 Hours

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Solving the Problem by Using a Table TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles35 Miles75 Miles 1 Hour80 Miles70 Miles150 Miles 1 ½ Hour120 Miles105 Miles225 Miles 2 Hours

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Solving the Problem by Using a Table TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles35 Miles75 Miles 1 Hour80 Miles70 Miles150 Miles 1 ½ Hour120 Miles105 Miles225 Miles 2 Hours160 Miles140 Miles300 Miles

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TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles 80 (0.5) 35 Miles 70 (0.5) 75 Miles 1 Hour80 Miles70 Miles150 Miles 1 ½ Hour120 Miles105 Miles225 Miles 2 Hours160 Miles140 Miles300 Miles

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TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles 80 (0.5) 35 Miles 70 (0.5) 75 Miles 1 Hour80 Miles 80 (1) 70 Miles 70 (1) 150 Miles 1 ½ Hour120 Miles 80 (1.5) 105 Miles 70 (1.5) 225 Miles 2 Hours160 Miles 80 (2) 140 Miles 70 (2) 300 Miles

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TimeDistance Truck Drove Distance Car Drove Total Distance ½ Hour40 Miles 80 (0.5) 35 Miles 70 (0.5)75 Miles 1 Hour80 Miles 80 (1) 70 Miles 70 (1)150 Miles 1 ½ Hour120 Miles 80 (1.5) 105 Miles 70 (1.5)225 Miles 2 Hours160 Miles 80 (2) 140 Miles 70 (2)300 Miles Rate (Time) + Rate (Time) = Total Distance += += + = +=

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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

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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 2 Hours

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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

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Fin

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