1. Algebra Motion Problems (Rate-Time-Distance)

2. The Formula Rate ● Time = Distance Average speed Elapsed timeLinear Distance 50 mph ● 3 hours = 150 miles 50 50 50

3. The Formula So, it follows that since then and If you know any two, you can find the third if it is unknown.

4. Setting up the Equation: The 2 Types of Motion Problem Set-ups d 1 + d 2 = Total Distance Two people moving toward each other. Two people moving away from each other. d 1 = d 2 A person catching up. A round trip problem.

5. d 1 + d 2 = Total Distance rate * time + rate * time = Sum of distances This equation is used when the motion is in opposite directions, such as two vehicles moving towards each other or moving apart. The total distance covered is the sum of the two parts. d1d1 d2d2

6. At noon, Hans and Franz each started from their homes which are 16 miles apart and biked towards each other. Hans’ speed was 2 miles per hour faster than Franz’ speed. The boys met at 2pm. What was the speed of each bicyclist? Example:

7. At noon, Hans and Franz each started from their homes which are 16 miles apart and biked towards each other. Hans’ speed was 2 miles per hour faster than Franz’ speed. The boys met at 2pm. What was the speed of each bicyclist? Hans Franz r + 2 r d 1 + d 2 = 16 12:00 2:00 2(r + 2) + 2r = 16 2r + 4 + 2r = 16 4r + 4 = 16Franz: 3 mph 4r = 12Hans:5 mph r = 3 Let r = Franz’s rate

8. d 1 = d 2 rate * time = rate * time This equation is used when the motion is in the same direction, such as one vehicle overtaking another. The total distance covered is the same. This is also used to describe a round trip. d1d1 d2d2 d1d1 d2d2

9. At 4 pm, Mrs. Regalia took off in her Ferrari from SRVHS heading towards San Diego at a speed of 60 miles per hour. One hour later, Mr. Willis took off from SRVHS in his RAV4 on his way to San Diego at a speed of 70 miles per hour. At what time did Mr. Willis catch up to Mrs. Regalia on the freeway? Example:

10. At 4 pm, Mrs. Regalia took off in her Ferrari from SRVHS heading towards San Diego at a speed of 60 miles per hour. One hour later, Mr. Willis took off from SRVHS in his RAV4 on his way to San Diego at a speed of 70 miles per hour. At what time did Mr. Willis catch up to Mrs. Regalia on the freeway? d 1 = d 2 60t =70(t-1)Mr. Willis caught up 7 60t =70t – 70hours after Mrs. Regalia -10t =-70left. It was 11pm. t =7 4pm 60 mph d 1 5pm 70 mph d 2 Let t = the time Mrs. Regalia drove.

11. Mr. Hunter drove from his house to Lake Tahoe at 70 miles per hour. The trip home took him longer because of heavier traffic and he was only able to travel at 50 miles per hour. If it took him 1 hour longer to return than to go, how many hours did the drive home take? Example:

12. Mr. Hunter drove from his house to Lake Tahoe at 70 miles per hour. The trip home took him longer because of heavier traffic and he was only able to travel at 50 miles per hour. If it took him 1 hour longer to return than to go, how many hours did the drive home take? d 1 = d 2 70t =50(t+1) The drive home took Mr. 70t =50t + 50 Hunter 3½ hours.That is 20t = 50 one hour longer (t+1) than t = 5/2 or 2½ the drive there. d2d2 d1d1 70 mph t 50 mph t + 1 Let t = the time it took to drive to Tahoe

13. Homework Motion Problem W/S #1