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.

Problem 6

Two jet planes left Naria Airport at 9:00 am and travels in opposite directions. One jet travels at an average speed of 450 kilometers per hour and the other jet travels at an average speed of 550 kilometers per hour. By what time will the two jets be 2500 kilometers apart?

Solution 1

Just like in the previous parts, we can solve this problem using a table. As we can see, in the first hour, the jets will be 1000 kilometers apart. After three hours they will be 3000 kilometers apart.

motion problems opposite direction

 

The question, however, is the time when they are 2500 kilometers. From the table above, since after each hour, the distance traveled is 1000 kilometers, then 2500 kilometers will require 2 and a half hours. Now, 2 and a half hours after 9 am is 11:30 am.

Solution 2

We name the jet planes A and B as shown below. Plane A travels at 450 kilometers per hour and plane B at 550 kilometers per hour. The time traveled by both planes, we let x and since they both start and the same time, they will have the same time (duration) traveled. The distance d is the product of the rate and the time.

Note: The time of departure so (9:00 am) is irrelevant at first in solving the problem. It can only be used after the answer is obtained.

 Screen Shot 2014-03-31 at 2.02.49 PM

Now that we have the table, let us examine the figure below.  In the question, how many hours will the two planes be 2500 kilometers apart. Since the planes are traveling in opposite directions, the word “apart” in the problem means the distance traveled by the first plane (450x) and the distance traveled by the second plane (550x). Therefore, we can form the equation

d traveled by Plane A + d traveled by plane B = 2500

Screen Shot 2014-03-31 at 2.17.14 PM

If we substitute the values in the table in the preceding equation, then we have

450x + 550x = 2500

1000x = 2500

x = 2.5 hours

Meaning, if the planes are 2500 kilometers apart, two and a half hours would have past. Therefore, 2 and a half hours from the time of the departure which is 9:00 am is 11:30 am.

Therefore the correct answer is 11:30 am. This confirms the answer in Solution 1.

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