1. Algebra 1
Section 3.7

2. Uniform Motion
Uniform motion problems involve one or more objects traveling at constant speed.
Formula: d = rt

3. Be sure to use the right units!
d = rt
rate × time = distance r t = d 50 45 3 t 5 =
150
50t
225
Be sure to use the right units!

4. Example 1 Both groups travel the same distance.
The high school travels at 5 mi/hr for an “unknown” time [x].
The junior high travels at 3 mi/hr for one hour longer than the high school [x + 1].

5. Since the distances are equal:
Example 1 r t = d
junior high
high school 3 5
t + 1 t =
3(t + 1) 5t
Since the distances are equal:
3(t + 1) = 5t

6. Example 1 3(t + 1) = 5t 3t + 3 = 5t 3 = 2t t = 1½
The high-school class needs 1½ hours to catch up with the junior-high class.

7. Solving Uniform Motion Problems
Read the problem carefully.
Plan a strategy.
Solve an equation.
Check.

8. For both trains, t = 3 hours
Example 2
Northbound train
rate = r + 5
Total distance: 333 mi.
Mattoon
Southbound train
rate = r
For both trains, t = 3 hours

9. Since total distance is 333 mi:
Example 2 r t = d
northbound
southbound
r + 5 r 3 =
3(r + 5) 3r
Since total distance is 333 mi:
3(r + 5) + 3r = 333

10. Example 2 3(r + 5) + 3r = 333 3r + 15 + 3r = 333 6r + 15 = 333

11. Example 2
r = 53
The southbound train travels at a rate [r ] of 53 mi/hr.
The northbound train travels at a rate [r + 5] of 58 mi/hr.

12. Example 3 Both runners run for the same amount of time [t ].
Jon travels 400 m more than Paul.
Jon’s distance
Paul’s distance
400

13. Since Jon’s distance is 400 m greater than Paul’s distance:
Example 3 r t = d
Jon
Paul
375
325 t =
375t
325t
Since Jon’s distance is 400 m greater than Paul’s distance:
375t = 325t + 400

14. Example 3
375t = 325t + 400
50t = 400
t = 8 minutes

15. Example 3 t = 8 minutes Both runners ran for 8 minutes.
Jon ran 375(8) = 3000 m, which equals 7.5 laps.
Paul ran 325(8) = 2600 m, which equals 6.5 laps.

16. Homework: pp