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3.4. Rates. 1.Solve problems involving two objects traveling in opposite directions. 2.Solve problems involving two objects traveling in the same direction. Rate Problems. distance = rate ∙ time. distance = distance d = d. same direction. opposite directions.

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Rates

3.4

Rates

1.Solve problems involving two objects traveling in opposite directions.

2.Solve problems involving two objects traveling in the same direction.


Rates

Rate Problems

distance = rate ∙ time

distance = distance

d = d

same direction

opposite directions

distance 1 + distance 2 = total distance

d1 + d2 = dt

Find rate and time for each vehicle.


Rates

Rate Problems

What did we find?

Did we answer the question?

Two trains are traveling on parallel tracks toward each other from a distance of 533 miles. If the freight train is traveling at 27 miles per hour and the passenger train is moving at 55 miles per hour, how long will it take for them to meet each other?

d1 + d2 = dt

d = d

55t + 27t =

533

82t = 533

27 mph

55 mph

t = 6.5

533 miles

The trains will meet in 6.5 hours.

d = r t

55 mph

= 6.5

t

55t

27t

27 mph

t


Rates

Rate Problems

What did we find?

Did we answer the question?

Two planes leave Denver at the same time, one flying north and the other flying south. If the plane flying south is traveling at 653 miles per hour and the plane flying north is traveling 560 miles per hour, after how many hours will the planes be 2426 miles apart.

d1 + d2 = dt

d = d

653t + 560t =

2426

1213t = 2426

653 mph

560 mph

t = 2

2426 miles

The planes will be 2426 miles apart in 2 hours.

d = r t

653 mph

t

653t

= 2

560t

560 mph

t


Rates

Morrison leaves Cincinnati at 4:00 pm, heading for NYC. Barbara leaves at 4:30 pm on the same highway, heading toward NYC. By driving 10 mph faster, Barbara overtakes Morrison at 7:30 pm. How fast is Barbara driving and how far have they traveled when Barbara catches up with Morrison?

d1 + d2 = dt

d = d

4:00

M

3.5r = 3(r + 10)

B

+ 10 mph

4:30

3.5r = 3r + 30

Be sure you answer the question that is asked!!

35r = 30r + 300

What did we find?

5r = 300

Did we answer the question?

r = 60

How fast is Barbara driving?

60 + 10 = 70 mph

r + 10 =

How far have they traveled?

d = rt

210 miles

= (70)(3) =

d = r t

r

= 60

3.5

3.5 r

3(r + 10)

r + 10

= 70

3


Rates

Rate Problems

What did we find?

Did we answer the question?

Monica and Chandler pass each other along a straight road traveling in opposite directions. Monica is driving at 40 mph and Chandler at 50 mph. In how many hours will the cars be 225 miles apart?

Monica

Chandler

d1 + d2 = dt

d = d

50 mph

40 mph

40t + 50t =

225

90t = 225

225 miles

t = 2.5

They will be 225 miles apart in 2.5 hours.

d = r t

40 mph

t

= 2.5

40t

50t

50 mph

t


Rates

At 6 a.m. a freight train leaves Washington D.C. traveling at 50 mph. At 9 a.m. a passenger train leaves the same station traveling in the same direction at 75 mph. How long will it take the passenger train to overtake the freight train? How far from the station will they be at that time?

d1 + d2 = dt

d = d

6:00

50 mph

50t = 75(t – 3)

Freight train

9:00

75 mph

50t = 75t – 225

Passenger train

– 25t = – 225

What did we find?

t = 9

Did we answer the question?

How long will it take for the passenger train to overtake the freight train?

6 hours

How far from the station will they be at that time?

d = rt

450 miles

= (50)(9) =

d = r t

50

= 9

t

50t

75(t – 3)

75

t – 3

= 6


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