MOTION PROBLEMS

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.