Motion Word Problems
Students will solve motion problems by
using a Guess & Check Chart and
Algebra
D = R x T Review

Motion Problems use the formula
Distance = Rate x Time
If the rate is 60 mph and
the time is 3 hours, what is
the distance?
If the distance is 300 miles
and it took 4 hours, what
was the rate of speed?
If the distance is 200 miles
and the rate is 40 mph,
what is the time?
If the time was 2.5 hours
and the rate was 40 mph,
what was the distance?
What’s involved in a motion
problem?
Two vehicles
A slower one
And a faster one!

What’s involved in a motion
problem?
Going in the same
direction.
Or opposite directions!!
What’s involved in a motion
problem?
Leaving at the
same time.
Leaving at different times
Step One: Draw the problem
It helps to find the distance needed to solve the problem.
Look for: Starting Point,Direction, Departure Time
Draw: Ex 1. Two cars start at the same point, at the
same time, and travel in opposite directions. The
slow car travels at 56 mph and the fast car travels at
60 mph. In how many hours, will they be 464 miles
apart? Slow Car (56 mph)
Fast car (60 mph)
Slow Car Distance + Fast Car Distance = 464
Drawing Practice
Ex. 2 Two trains start at the same time from stations that were
360 miles apart and travel towards each other. The rate of the
fast train exceeded the rate of the slow train by 10 miles per
hour. At the end of 2 hours, the trains were still 120 miles
apart. Find rate of each train.
Starting Pt: 360 miles apart.
Direction: Towards each other
Starting Time: Same
Fast Train
120 miles
Slow Train
Total Distance: 360 miles
Fast Distance + Slow Distance + 120 = 360 or
Fast Distance + Slow Distance = 240
Drawing Practice
Ex 3. How far can a man drive out into the country at
the average rate of 60 miles per hour and return
over the same road at 45 miles per hour if he travels
a total of 7 hours. Starting Pt: Home & Unknown
Direction: Away and back
home
Starting Time: A total of 7
hours
Fast Rate
Slow Rate
Fast Distance = Slow Distance
Step 2: Make A Chart
Slow Slow Slow Fast Fast Fast Distance
Rate Time Dist Rate Time Dist Equation
Ex 1. Two cars start at the same point, at the same
time, and travel in opposite directions. The slow car
travels at 56 mph and the fast car travels at 60 mph.
In how many hours, will they be 464 miles apart?
Fill in: What you know
Slow
Rate
Slow
Time
Slow
Dist
Fast
Rate
Fast
Time
Fast
Dist
Distance
Equation
SD + FD = 464
56
60
Which is the “GUESS” column?
Hours
Ex 1. Two cars start at the same point, at the same
time, and travel in opposite directions. The slow car
travels at 56 mph and the fast car travels at 60 mph.
In how many hours, will they be 464 miles apart?
Guess: 2 hours and fill in rest of chart
Slow
Rate
Slow
Time
Slow
Dist
Fast
Rate
Fast
Time
Fast
Dist
Distance
Equation
SD + FD = 464
56
2
112
60
2
120
112+120 = 232
No
Ex 1. Two cars start at the same point, at the same
time, and travel in opposite directions. The slow car
travels at 56 mph and the fast car travels at 60 mph.
In how many hours, will they be 464 miles apart?
Try more Guesses
Slow Slow Slow Fast Fast Fast
Rate Time Dist Rate Time Dist
56
2
112
60
2
120
56
5
280
60
5
300
56
4
224
60
4
240
Distance
Equation
SD + FD = 464
112+120 = 232
No
280+300=580
No
224+240=464
YES!
IN 4 HOURS, THEY WILL BE 464 MILES APART
Using Algebra
Use Guess & Check Chart to convert
to an Algebra problem
 Place x in Guess Column. Fill in rest of
row
 Define variables
 Write & Solve Equation
 Answer Question!

Ex 1. Two cars start at the same point, at the same
time, and travel in opposite directions. The slow car
travels at 56 mph and the fast car travels at 60 mph.
In how many hours, will they be 464 miles apart?
Slow Slow Slow Fast Fast Fast
Rate Time Dist Rate Time Dist
56
4
224
60
4
240
56
X
56x
60
X
60x
Let x = # of hours
Distance
Equation
SD + FD = 464
224+240=464
YES!
56x+60x=464
56x+60x=464
116x=464
X=4
Answer: It
took four
hours.
Ex. 2 Two trains start at the same time from stations
that were 360 miles apart and travel towards each
other. The rate of the fast train exceeded the rate of
the slow train by 10 miles per hour. At the end of 2
hours, the trains were still 120 miles apart. Find
rate of each train.
Fill in what you know and find Guess Column
Slow Slow Slow Fast Fast Fast Distance
Rate Time Dist Rate Time Dist Equation
SR+10
2
SD+FD=240
2
Guess: Slow Rate
Fast Rate = Slow Rate + 10
Ex. 2 Two trains start at the same time from stations
that were 360 miles apart and travel towards each
other. The rate of the fast train exceeded the rate of
the slow train by 10 miles per hour. At the end of 2
hours, the trains were still 120 miles apart. Find
rate of each train.
KEEP GUESSING
Slow Slow Slow Fast Fast Fast Distance
Rate Time Dist Rate Time Dist Equation
SR+10
SD+FD=240
50
2
100
60
2
120
100+120=220
60
2
120
70
2
140
120+140=260
55
2
110
65
2
130
110+130=240
Slow Train Rate: 55
Fast Train: 65
Ex. 2
On to ALGEBRA
X is in Guess column
SR
ST
SD
FR
FT
FD
SR+10
55
X
2
2
110 65
2
2X X+10 2
Dist Equ
SD+FD=240
130
110+130=240
2(X+10) 2X+2(X+10)=240
Let x = slow rate
2x+2(x+10) = 240
Let x + 10= Fast rate
2x + 2x + 20 = 240 Answer:
Slow Train:
4x+20 = 240
55 mph
4x = 220
Fast Train:
X = 55
65 mph
Ex 3. How far can a man drive out into the
country at the average rate of 60 miles per
hour and return over the same road at 45
miles per hour if he travels a total of 7 hours.
Fill in what you know and find Guess Column
Slow Slow Slow Fast Fast Fast Distance
Rate Time Dist Rate Time Dist Equation
SD=FD
Guess: Slow Time
Slow Time + Fast Time = 7
Ex 3.
SR
ST
SD
FR
FT
FD
Distance
Equation
SD=FD
45
45
45
45
5
4
3
X
225
180
135
45x
60
60
60
60
2
3
4
(7-x)
120
180
240
60(7-x)
225=120
180=180
135=240
45x=60(7-x)
Let x =
Slow Time
45x=60(7-x)
Answer the Question!
45x=420-60x
Let 7-x =
Fast Time
105x=420
The man drove out
180 miles
X=4
Wrapping It UP- Motion

Distance Formula :

D=rxt

Why is it necessary
to draw picture?

To find Distance
Equation

Where does the x
go in the Guess and
Check chart?

In the Guess
column