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How FAST should I travel to reach her?!. MOTION PROBLEMS. What TIME will he arrive? . How FAR is his office from my house?. RATE. the ratio between distance and time. D. ______. =. R. T. RATE. D. D. _____. R. =. T. R. T. DISTANCE. D. D. =. R. x. T. R. T. TIME. - PowerPoint PPT Presentation
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How FAST should I travel to
reach her?!
How FAR is his office from my house?
What TIME will he
arrive?
MOTION PROBLEMS
RATE the ratio between distance and time
R = ______D
T
T
D
R
R =D_____T
RATE
T
D
R
D = R
DISTANCE
x T
T
D
R R=
D_____T
TIME
PROBLEM NO. 1Dr. Reyes drove from his home to a
medical mission at the rate of 65 kph. In going home, tired from work, he drove at the rate of 50 kph. If it took him one hour more in going home than in going to the mission, how far is the mission site from his home? (Assume that he passed through the same road).
Table for Representation
From his home to
the medical mission
From the medical
mission to his home
Rate (kph) Time (hrs) Distance (km)
65
50
x
x + 1
65x
50 (x + 1)
BACK to the PROBLEM
FORMULA?
EQUALS
65 x
50 (x + 1)
FOR THE WORKING EQUATION:
SOLUTION:
65x = 50x + 5015x = 50
x = 5015
x = 10 3
65x = 50 (x + 1)
hours
BACK to the REPRESENTATION
DISTANCE = ?
D = 65x
65=
= 650 3
= km
The mission site is
km from the
house.
PROBLEM NO. 2Clarissa’s office is 28 km from her house.
Upon reaching the office, she realized she forgot her cell phone. Since she is expecting a very important call from her client, Paolo, she decided to go back home and get it. At home, however, her grandma noticed the phone and asked Clarissa’s mom to go to Clarissa’s office to give it. If they live their respective places at the same time, and Clarissa is traveling 80 kph and her mom at 60 kph, after how many hours will they meet on the road? (Assume they will use the same road.)
Table for RepresentationRate (kph) Time (hrs) Distance (km)
Clarissa
Mom
80 x 80 x
60 xx60
BACK to the PROBLEM
FOR THE WORKING EQUATION:
28 km
80 x60 x
= 28 km80 x60 x +
SOLUTION:
80 x + 60 x = 28140 x = 28
x = 28 140
x = 1 5
hour Or12 minutes
Clarissa and her mom will meet after 12 minutes.
BACK to the REPRESENTATION
PROBLEM NO. 3Jaime and Pearl left their home and traveled in
opposite directions. Jaime went to his client and drove at the rate of 72 kph and Pearl drove at 54 kph to school. When will they be 168 km apart?
168 km
Table for Representation
Jaime
Pearl
Rate (kph) Time (hrs) Distance (km)
72
54
x 72 x
x 54 x
BACK to the PROBLEM
FOR THE WORKING EQUATION:
168 km
72 x 54 x
72 x + 54 x 168=BACK to the PROBLEM
SOLUTION:
72 x + 54 x 168=
126 x = 168
x = 168126
x = 43
or hours
Jaime and Pearl will be 168 km apart after
hours (1 hour and 20 minutes).
BACK to the REPRESENTATION
PROBLEM NO. 4
Ms. Buenavides was in a hurry when she left her office to attend a meeting. She instructed her driver to drive at the rate of 60 kph. Her assistant head, Mr. Dabuet, followed after 1 hour traveling at the rate of 84 kph. When will Mr. Dabuet overtake Ms. Buenavides if they started at the same place and used the same path?
A F T E R 1 H O U R:
Table for Representation
Ms. Buenavides
Mr. Dabuet
Rate (kph) Time (hrs) Distance (km)
60
84
x + 1 60 (x + 1)
x 84 x
BACK to the PROBLEM
FOR THE WORKING EQUATION:
60 (x + 1)
84 xE Q U A L S
=60 (x + 1) 84 x
SOLUTION:
=60 (x + 1) 84 x
60 x + 60 = 84 x
60 = 24 x
x = 6024
x = 52
or hoursBACK to the REPRESENTATION
After traveling for hrs, Dr. Dabuet will
overtake Dr. Buenavides.