1. Rational Expressions Chapter 10
Distance – Rate - Time H W Q T

2. Motion Problems d = r t The Distance Formula:
Motion problems involve distance, time and rate.
The equation that links these concepts is called
The Distance Formula:
miles/hour
km/min.
m/s
ft./sec.
inches/sec.
hours
minutes
seconds
days
years
miles
kilometers
meters
feet
inches
d = distance
d = r t
r = rate
t = time

3. Motion Problems d = r t The Distance Formula:
Motion problems involve distance, time and rate.
The equation that links these concepts is called
The Distance Formula:
miles/hour
km/min.
m/s
ft./sec.
inches/sec.
d = distance
d = r t
t = time
r = rate
You’ll need to be comfortable
with using and manipulating
the distance formula.

4. Rational Expressions Chapter 10
Distance – Rate - Time

5. Here is a strategy to solve motion problems
1. Read the problem (three times) picking out key information
2. Draw a diagram of what is happening.
3. Make a table that relates distance, rate and time.
4. Use the table to write an equation.
Distance = rate x time
5. Answer the question – include the units!

6. Example 1
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.
x = speed of walker
x + 8 = speed of cyclist
18 miles
54 miles
Distance = rate x time
Walker 18
Biker 54

7. Example 1
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.
Time
Walker
Time
Biker
Distance = rate x time
Walker 18
Biker 54

8. Example 1
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.

9. # 2
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.
180
240
x = speed of red (slower) car
Distance = rate x time
Slow car
180 x
240
x + 20
Fast car

10. 180 240 Time Time Slow Fast Car Car x x + 20
# 2
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.
Time
Slow
Car
Time
Fast
Car
x = speed of red (slower) car
Distance = rate x time
Slow car
180 x
240
x + 20
Fast car

11. # 2
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.

12. An airplane can fly at a speed of 240 m.p.h. in calm air.
Example 3
An airplane can fly at a speed of 240 m.p.h. in calm air.
It takes the same time to fly 1080 miles with the wind
as it does 840 miles against the wind. Find the speed
of the wind.
speed in “calm air” = 240
d = 1080 miles
w = ?
Wind
d = 840 miles

13. An airplane can fly at a speed of 240 m.p.h. in calm air.
Example 3
An airplane can fly at a speed of 240 m.p.h. in calm air.
It takes the same time to fly 1080 miles with the wind
as it does 840 miles against the wind. Find the speed
of the wind.
Let w = speed of wind
Distance = rate x time
With
1080
240 + w
Against
840
240 - w
Time
with
wind
Time
against
wind

14. Homework #1
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. #2
One car travels 40 km/h faster than another. While one travels 150 km, the other goes 350 km. Find their speeds. #3
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. #4
A person traveled 120 miles in one direction. The return trip was accomplished at double the speed and took 3 hours less time. Find the speed going