Help! Word problem!

Question

Two cars leave towns 45 kilometers apart at the same time and travel toward each other. One car's rate is 18 kilometers per hour less than the other's. If they meet in 3 hours, what is the rate of the slower car?

Answer 1

We'll use distance = (rate)(time) to solve this problem.

 

First, let's think about Car A. This will be the slower car. We're not told how far it traveled, so let's call its distance d. We're not told how fast it traveled, so let's call its rate r. We do know that it traveled for 3 hours before it met the other car, so time = 3.

 

Car A's equation: d = 3r

 

Now, let's think about Car B. We're not told how far it traveled, but we know that together, the cars traveled 45 kilometers, so its distance = 45 - d. We're not told how fast it traveled, but we know that it traveled 18 kph faster than the slower car, so its rate = r + 18. We do know that it traveled for 3 hours before it met the other car, so time = 3.

 

Car B's equation: 45 - d = 3(r + 18)

 

 

Let's plug d = 3r into Car B's equation and solve for r (which is the rate of the slower car):

 

45 - 3r = 3(r + 18)

45 - 3r = 3r + 54

45 - 6r = 54

-6r = 9

r = -9/6

r = -3/2

 

 

That's a pretty weird answer. That's because the towns are 45 kilometers apart, which means that, if the cars really took 3 hours to reach each other and one was traveling 18 kph faster than the other, the faster car had to have gone past the other town. So, the slower car must have driven backwards, hence the rate of -3/2 kph.

 

You should check the numbers in your problem. Perhaps you meant to say that the towns were 450 kilometers apart, not 45 kilometers apart. If that's the case, the same steps for finding a solution will work, just use 450 instead of 45. You should get a much more reasonable rate.