warm up multiply #4 #1#2 #3 add solve. warm up # 1 multiply
TRANSCRIPT
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.?