SOLUTION: Two cars, A and B, are traveling along the same road at an average speed of 48 kph and 40 kph respectively. When A is 16 km from town C along the road, B is 12 km from C. A passed

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Question 205860: Two cars, A and B, are traveling along the same road at an average speed of 48 kph and 40 kph respectively. When A is 16 km from town C along the road, B is 12 km from C. A passed B "x" km from c. Find x and interpret the result.
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
There are several ways to approach this problem. The one that is 'easiest' for me to think through ask the following questions.
1) Given the two cars current distances from each other and the knowing their relative speeds, how long will it take for the two cars to be at the same point?
Car A is 16 km from the town. Car B is 12km. So the two cars are 4km apart.
Car A is traveling 48kpm. Car B is going 40 kph in the exact same direction. So A is going 8kpm faster than B.
How long will it take for the two cars to be at the same point?

It will take car A one half hour (30 minutes) to catch up to car B. So 'x' in your original question is 30 minutes.

2) Where will the cars be when A passes B?
For this question, you need to find out how far one or the other car goes in 1/2 hour.
Again, use the same basic equation

Let's use Car A

So car A will have moved 24 km.
Note you could have used Car B too. In that case

So car B will have moved 20 km.
Now, take the location of A and add 24 to it.

So the cars pass each other 8km after they pass through town C.
You can do the same process on car B to see it is also at 8km beyond C.

You could setup equations and model it that way. Your teacher might prefer it.

So

For B

Set the two locations equal and solve for Time. You get the same result. It is quicker to use modeling; but that assumes you understand the idea behind it already.