1. D = R x T Review 180 miles 75 mph 5 hours 100 miles
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?
180 miles
75 mph
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?
5 hours
100 miles

2. What’s involved in a motion problem?
Two vehicles
A slower one
And a faster one!

3. What’s involved in a motion problem?
Going in the same direction.
Or opposite directions!!

4. What’s involved in a motion problem?
Leaving at the same time.
Leaving at different times

5. 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)
Start
Total Miles: 464 miles
Slow Car Distance + Fast Car Distance = 464

6. Drawing Practice Starting Pt: 360 miles apart.
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
120 miles
Fast Train
Slow Train
Total Distance: 360 miles
Fast Distance + Slow Distance = or
Fast Distance + Slow Distance = 240

7. Fast Distance = Slow Distance
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
Start
Slow Rate
Fast Distance = Slow Distance

8. 50 100 60 120 100+120=220 Slow Rate Time Dist Fast Distance Equation 2
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
Rate
Time
Dist
Fast
SR+10
Distance
Equation
SD+FD=240 2 50
100 60
120
=220
Guess: Slow Rate
Fast Rate = Slow Rate + 10

9. Slow Rate Slow Time Slow Dist Fast Rate Fast Time Fast Dist Distance
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
Rate
Slow
Time
Slow
Dist
Fast
Rate
SR+10
Fast
Time
Fast
Dist
Distance
Equation
SD+FD=240 50 2
100 60 2
120
=220 60 2
120 70 2
140
=260 55 2
110 65 2
130
=240
Slow Train Rate: 55 Fast Train: 65

10. SR ST SD FR FT FD Dist Equ 55 2 110 65 2 130 X 2 2X X+10 2 Ex. 2
On to ALGEBRA
X is in Guess column SR ST SD FR
SR+10 FT FD
Dist Equ
SD+FD=240 55 2
110 65 2
130
=240 X 2 2X
X+10 2
2(X+10)
2X+2(X+10)=240
2x+2(x+10) = 240
2x + 2x + 20 = 240
4x+20 = 240
4x = 220
X = 55
Let x = slow rate
Let x + 10= Fast rate
Answer:
Slow Train: 55 mph
Fast Train:
65 mph

11. 225=120? 225 60 2 120 45 5 Slow Rate Time Dist Fast Distance Equation
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
Rate
Time
Dist
Fast
Distance
Equation
SD=FD
225=120?
225 60 2
120 45 5
Guess: Slow Time
Slow Time + Fast Time = 7

12. SR ST SD FR FT FD Distance Equation 45 5 225 60 2 120 225=120 4 180 3
Ex 3. SR ST SD FR FT FD
Distance
Equation
SD=FD 45 5
225 60 2
120
225=120 4
180 3
180=180
135
240
135=240 X
45x
(7-x)
60(7-x)
45x=60(7-x)
45x=60(7-x)
45x=420-60x
105x=420
X=4
Answer the Question!
The man drove out 180 miles
Let x = Slow Time
Let 7-x = Fast Time

13. Wrapping It UP- Motion Distance Formula :
Why is it necessary to draw picture?
Where does the x go in the Guess and Check chart?
D = r x t
To find Distance Equation
In the Guess column