1. 4 minutes
Warm-Up
Morgan is 9 years older than Emma. The sum of their ages is 43. How old are they?

2. Objectives: To solve problems involving uniform motion
Motion Problems
Objectives:
To solve problems involving uniform motion

3. Motion
distance = rate x time

4. Example 1 distance rate time Bud Carrie d 2 t + 1 d 3 t d = 2(t + 1)
Bud takes a leisurely stroll He walks at a constant rate of two miles per hour. Carrie starts out for a brisk walk one hour later. She walks at a constant rate of 3 miles per hour. How long will it take for Carrie to catch up with Bud?
distance
rate
time
Bud
Carrie d 2
t + 1 d 3 t
d = 2(t + 1)
d = 3t
2(t + 1) = 3t
2t + 2 = 3t
2 = t
after Carrie walks for 2 hours

5. Practice
A car leaves Lompoc traveling north at 56 km/h. Another car leaves Lompoc one hour later traveling north on the same road at 84 km/h. How far from Lompoc will the second car overtake the first?

6. Example 2 distance rate time Kathy Gilbert d 55 t 553 - d 35 11.4 - t
Kathy and Gilbert drove a total of 553 miles in 11.4 hours. Kathy drove the first part of the trip and averaged 55 miles per hour. Gilbert drove the second part of the trip and averaged 35 miles per hour. For what length of the time did Kathy drive?
distance
rate
time
Kathy
Gilbert d 55 t
553 - d 35 t
d = 55t
20t = 154
553 – d = 35 (11.4 – t)
t = 7.7
553 – 55t = 35(11.4 – t)
553 – 55t = 399 – 35t
Kathy drove for 7.7 hours

7. Practice
Jen and Brian drove a total of 604 miles in 12.2 hours. Jen drove the first part of the trip and averaged 55 miles per hour. Brian drove the second part of the trip and averaged 45 miles per hour. For what length of the time did Jen drive?