Warm Up

Multiply

#4

3 x 4

x 4 3

3 x 4

x 4 3

3 x 4

x 4 3

2

1 3 12 2m m

#1 #2 #3

Solve

Add Solve

Warm Up

# 1

3 x 4

x 4 3

1

Multiply

Warm Up

# 2 Add

3 x 4

x 4 3

3 x 4

x 4x 4

9 2x 8x 16

2x 8x 253x 12

33

Warm Up

# 3 Solve

3 x 4

x 4 3

9 x 4 x 4

29 x 8x 16

20 x 8x 7

0 x 7 x 1 x 7,1

Warm Up

# 4

2

1 3 12 2m m

22

1 3 12 2m

mm

2

2m 3m 2 2m 3m 2 0

m 1 m 2 0

m 1, 2

Solve

Distance – Rate - Time Problems

d r t Distance Formula

drate

t d

timer

Rational Equations

Distance = rate x time

Biker

Walker

54 miles

18 miles

x = speed of walker

x + 8 = speed of cyclist

54

1818x54

x 8x 8

x

Rational Equations

dtime

r

A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

# 1

Rational Equations

TimeWalker

TimeBiker

18x

54x 8

Distance = rate x time

Biker

Walker

x = speed of walker

x + 8 = speed of cyclist

54

1818x54

x 8x 8

xd

timer

A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

# 1

54x 8

Rational Equations

18x

18 x 8 54x

18x 144 54x

144 36x4 x

Walker 4 m.p.h.

Cyclist 12 m.p.h.

x = speed of walker

x + 8 = speed of cyclist

A bicyclist travels 8 miles per hour faster than a walker. The cyclist travels 54 miles in the same time it takes the walker to walk 18 miles. Find their speeds.

# 1

One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds.

# 2

Distance = rate x time

240

x + 20

x180

240

x = speed of red (slower) car180

180x

240x 20

Slow car

Fast car

x + 20 = speed of green (faster) car

Rational Equations

One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds.

# 2

x = speed of red (slower) carx + 20 = speed of green (faster) car

Distance = rate x time

x + 20

x180

240

180x

240x 20

Slow car

Fast car

TimeSlowCar

TimeFastCar

180x

240x 20

Rational Equations

One car travels 20 mph faster than the other car. While the faster car goes 240 miles the other car travels 180 miles. Find their speeds.

# 2

x = speed of red (slower) carx + 20 = speed of green (faster) car

180x

240x 20

Slow car 60 m.p.h.

Fast car 80 m.p.h.

180 x 20 240x

180x 3600 240x

3600 60x60 x

Rational Equations

Rational Equations

# 3

x = speed of the Vespa

2x = speed of the car

Distance = rate x time

2x

x120

120

120x

1202x

Vespa

Car

120 120x 2x

120 120

3x 2x

Jerry rode his Vespa 120 miles to Lakeville to visit his cousin. Jerry borrowed his cousin’s car and his return trip was accomplished at twice the speed and took 3 hours less time. Find the average speed of Jerry’s Vespa going to his cousin’s house.

Rational Equations

# 3

x = speed of the Vespa

2x = speed of the car120 120

3x 2x

120 120

3x 2

2xx

240 120 6x

120 6x20 x

Vespa 20 m.p.h.

Jerry rode his Vespa 120 miles to Lakeville to visit his cousin. Jerry borrowed his cousin’s car and his return trip was accomplished at twice the speed and took 3 hours less time. Find the average speed of Jerry’s Vespa going to his cousin’s house.

The speed of a freight train is 14 km/h slower than the speed of a passenger train. The freight train travels 330 km in the same time that it takes the passenger train to travel 400 km. Find the speed of each train.

One car travels 40 km/h faster than another. While one travels 150 km, the other goes 350 km. Find their speeds.

A lab tested two high-speed trains. One travels 40 km/h faster than the other train. While one train travels 70 km, the other travels 60 km. Find their speeds.

#1#1

#2#2

#3#3

#4#4

HomeworkHomework

A freight train leaves Pleasanton at 6:00 a.m. and travels 180 miles to San Luis Obispo. A car leaves Pleasanton at 10:30 a.m. traveling 36 m.p.h. faster than the train and pulls into S.L.O. at the exact same time as the train arrives. Assuming that the distance the car traveled was the same as the train, what was the average speed of the car? What time did both the car and the train arrive in S.L.O.?