## PCSR Civil Service Exam Review Guide 11

After learning age problems in PCSR Review Guide 10, let us now learn motion problems. Motion problems are problems that deal with distance, rate, and time. Watch the videos below and read the articles. From Wednesday to Saturday this week, I will post 10-15 practice problems.

PART I: MATH
A. Videos

B. Articles

Part II: ENGLISH

A. Vocabulary

Civil Service Exam Vocabulary Review 10

B. Grammar

## Week 10 Review: Answers and Solutions

After learning how to solve motion problems, let’s answer some exercises and problems. In the solutions, we let d = distance, r = rate, and t = time.

Exercises

1.)   A car travels and average speed of 75 kph. If it traveled for 3.5 hours, what is the total distance traveled?

d = rt
d = (75 kph)(3.5 hrs) =
d = 262.5 km

2.) A bus traveled 4 hours from City A to City B which is 450 kilometers apart. What is its average speed?

d = rt
450 km = (4 hrs)(r)
r = (450 kph)/(4 hrs)
r = 112.5 km

Problem

1.) Two cars left City A at 8:00 am going to City B using the same route. Car 1 traveled at the average speed of 60 kph while Car 2 traveled at an average speed of 50kph. At what time were the two cars 25 kilometers apart?

Let x = time traveled by the two cars
60x – 50x = 25
10x = 25
x = 25/10
x = 2.5 hours

2.5 hours = 2hours and 30 mins
2 hours and 30 minutes after 8:00 am is 10:30 am.

2.) The road distance from Sapiro City to Lireo City is 195 km. Car 1 left Sapiro City going to Lireo City at an average speed of 70kph. Car 2 left City Lireo City going to Sapiro City at an average speed of 60 kph. If both cars left the two cities at the same time and use the same road, after how many hours will the two cars meet?

Car 1
Rate = 70kph
Time = x
Distance = 70x

Car 2
Rate = 60kph
Time = x
Distance = 60x

Total distance = 195kph

70x + 60x = 195
130x = 195
x = 195/130

x = 1.5hrs

3.) A red car left Vigan at 9:00 AM and traveled to Manila at an average speed of 45 kph. After one hour, a white car left the same place for Manila using the same route at an average speed of 60 kph. At what time will the white car overtake the red car?

RED CAR
Rate = 45kph
Time = x+1
Distance = 45(x+1)

WHITE CAR
Rage = 60kph
Time = x
Distance = 60x

60x = 45(x+1)
60x = 45x+45
60x – 45x = 45
15x = 45
x = 45/15
x = 3hours

3 hours after 10:00am is 1:00 p.m.

Note: We add 3 hours to 10:00 am because the second car left at 10:00 am.

4.) Two cars started from the same point, at 12nn, traveling to opposite directions at 50 and 60 kph, respectively. What is the distance between them at exactly 3:30 PM?

CAR 1
Rate = 50kph
Time = 3.5 hrs
Distance = (50 kph)(3.5 hrs) = 175

CAR 2
Rate = 60kph
Time = 3.5 hrs
Distance = (60 kph)( 3.5 hrs) = 210

What is the distance between them at exactly 3:30 PM?
175 km + 210 km = 385 km

5.) Two cars from the same point traveling to opposite directions at 75 and 85 kph, respectively. After how many hours will they be 240 kilometers apart?

75x + 85x = 240
160x = 240
240/160 = x
x = 1.5 hours

6.) A blue car leaves City A for City B at exactly 8:00 AM traveling at average speed of 55 kph. A gray car leaves City B for City A at the same time traveling at an average speed of 45 kph. The distance between the two cities is 75 kilometers.

If the two cars use the same route, what time will they pass each other?

let x be the time
d = r x t

sum of the distance traveled by 2 cars is equal to 75km
so

55x + 45x = 75
100x = 75
x = 75/100 or 0.75 hours
0.75 hours (45 mins)

They will pass each other 45 mins after 8:00am so the answer is 8:45 am.

Enjoy!

## Week 10 Review: Practice Exercises and Problems

After learning how to solve motion problems, let’s answer some exercises and problems.

Exercises

1.)   A car travels and average speed of 75 kph. If it traveled for 3.5 hours, what is the total distance traveled?

2.) A bus traveled 4 hours from City A to City B which is 450 kilometers apart. What is its average speed?

Problem

1.) Two cars left City A at 8:00 am going to City B using the same route. Car 1 traveled at the average speed of 60 kph while Car 2 traveled at an average speed of 50kph. At what time were the two cars 25 kilometers apart?

2.) The road distance from Sapiro City to Lireo City is 195 km. Car 1 left Sapiro City going to Lireo City at an average speed of 70kph. Car 2 left City Lireo City going to Sapiro City at an average speed of 60 kph. If both cars left the two cities at the same time and uses the same road, after how many hours will the two cars meet?

3.) A red car left Vigan at 9:00 AM and traveled to Manila at an average speed of 45 kph. After one hour, a white car left the same place for Manila using the same route at an average speed of 60 kph. At what time will the white car overtake the red car?

4.) Two cars started from the same point, at 12nn, traveling to opposite directions at 50 and 60 kph, respectively. What is the distance between them at exactly 3:30 PM?

5.) Two cars from the same point traveling to opposite directions at 75 and 85 kph, respectively. After how many hours will they be 240 kilometers apart?

6.) A blue car leaves City A for City B at exactly 8:00 AM traveling at average speed of 55 kph. A gray car leaves City B for City A at the same time traveling at an average speed of 45 kph. The distance between the two cities is 75 kilometers.

If the two cars use the same route, what time will they pass each other?

7.) A gray car leaves Batangas City for Quezon City at 11:00 am at an average speed of 50 kph. After one hour, a black car leaves Quezon City for Batangas at an average speed of 60 kph. If the two cars use the same route,  at exactly what time will the two cars pass each other?

Enjoy!

## PCSR REVIEW SERIES WEEK 10: Motion Problems

We have learned number problems and age problems. Now, we learn how to solve motion problems or problems involving distance, rate, and time. Below are the articles and videos that you can watch to learn about motion problems.

ARTICLES

VIDEOS

Enjoy!

## How to Solve Motion Problems Part 4

In Part 1, Part 2, and Part 3 of the How to Solve Motion Problems Series, we have learned how to solve problems involving objects moving in the same direction as well as those which move toward each other. In this post, we are going to learn about objects which move on opposite directions. The method in solving this problem is very similar to the method used in Part 3 of this series.

We now solve the sixth problem in this series. Continue Reading

## How to Solve Motion Problems Part 3

This is the third part of the How to Solve Motion Problems Series, a part of the Word Problem Solving Series of Ph Civil Service Reviewer. In Part 1 and Part 2 of this series, we discussed objects moving in the same direction. In this part, we are going to discuss objects moving toward each other. We have already discussed four problems in the previous parts of this series, so, we solve the fifth problem.

Problem 5

A car leaves City A and travels towards City B at an average speed of 60 kilometers per hour.  At the same time, another car leaves City B and travels towards city A at an average speed of 70 kilometers per hour. If the two cars use the same route, and if the distance between two cities is 520 kilometers, how many hours before they meet? Continue Reading

## How to Solve Motion Problems Part 2

This is the second part of the How to Solve Motion Word Problem series. I suggest that you read first the introduction to this series as well as the first part in order to understand better.

In the first part of this series, we discusses about a faster object overtaking a slower one who left first.  In this post, we continue to solve motion problems involving two objects traveling in the same direction and one object faster than the other; this time, they left at the same time. We want to know that given a particular time when they are a number of kilometers apart. Continue Reading

## How to Solve Motion Problems Part 1

Now that I have introduced to you motion problems, let us solve the type of problems that usually appear in textbooks as well as examinations. In this part of the series, we will learn how to analyze and solve a problem involving objects moving in the same direction. This is our third problem in the How to Solve Motion Problems Series.

Problem 3

Car A left Math City going to English City at an average speed of 40 kilometers per hour.  Two hours later, Car B traveling 60 kilometers per hour leaves the same place for English City. In how many hours, will the car B overtake Car A? Continue Reading

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