## 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?

Solution 1

Again, this problem can be solved using a table. By now, you would have realized that most motion problems can be solved by creating a table. You can use the table solution in case you cannot solve the motion problem algebraically. As we can see in the table above, for one hour, the two cars have traveled 130 kilometers toward each other. Since the distance between the two cities is 520 kilometers, it will take them four hours.

Solution 2

In the algebraic solution, it is also important to create a table as shown below. Shown on the columns are the rate, time, and distance. The car from City A travels at 60 kilometers per hour and the car from City B 70 kilometers per hour. The time they spend on the road is the same since they left the cities at the same time. Then, the distance they traveled is the product of the rate and the time. Note that at the exact time they meet, the would have traveled the total distance from A to B which is 520 kilometers. This means that if we add the distance they traveled, then the sum is 520 kilometers. From the discussion above, the equation is

d traveled by car from City A + d traveled by car from City B = 520 km.

Substituting the expressions on the table, we have $60x + 70x = 520$ $130x = 520$

Dividing both sides by 4, we have $x = 4$

Therefore, the two cars will meet in 4 hours after they have left the two cities.

Check

By the time they meet, the car from City A will have traveled 60(4) = 240 kilometers and car from City B will have traveled 70(4) = 280 kilometers. If you add the distance traveled by both cards, the answer is 520 kilometers. Therefore, we are correct.