Pamela Leutwyler. A B Town A is exactly 100 miles from Town B.

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Presentation transcript:

Pamela Leutwyler

A B Town A is exactly 100 miles from Town B

A B At noon train A leaves town A and travels toward town B at a rate of 20 mph

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph

Let’s replay the motion from the beginning

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet?

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) train A train B

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) train A train B fill in the information that is explicitly stated

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x 60 train A train B Let x represent the number of hours that train A travels

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x 60x - 1 train A train B Let x represent the number of hours that train A travels train B starts 1 hour later than train A if A travels for x hours then B travels for x - 1 hours

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x 60x - 1 train A train B

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x 60x - 1 train A train B formula: distance = (rate) x (time)

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x20x 60(x – 1)60x - 1 train A train B formula: distance = (rate) x (time)

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x20x 60(x – 1)60x - 1 train A train B distance traveled by train Adistance traveled by train B

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x20x 60(x – 1)60x - 1 train A train B distance traveled by train Adistance traveled by train B += 100

A B Town A is exactly 100 miles from Town B At noon train A leaves town A and travels toward town B at a rate of 20 mph At 1PM train B leaves town B and travels toward town A at a rate of 60 mph At what time do the trains meet? distanceratetime (# units of time) 20x20x 60(x – 1)60x - 1 train A train B distance traveled by train Adistance traveled by train B += x60(x – 1 )

A B Town A is exactly 100 miles from Town B At what time do the trains meet? distanceratetime (# units of time) 20x20x 60(x – 1)60x - 1 train A train B distance traveled by train Adistance traveled by train B += x60(x – 1 ) 20x + 60 ( x - 1 ) = x + 60x - 60 = x = 160 x = 2 train A starts at noon and travels for 2 hours before meeting train B 2 PM