Question

Two cars race around a circular track, in opposite directions, at constant rates. They start at the same position and meet every 30 seconds. If they move in the same direction, they meet every 120 seconds. If the track in 1800 meters long, what is the speed of each car?

Answer 1

• 22.5 m/s
• 37.5 m/s

Step-by-step explanation:

You want the speed of each car if they meet every 30 seconds on an 1800 m track when going in opposite directions, and every 120 seconds when going in the same direction.

Speeds

When the cars are moving in opposite directions, the speed at which they consume track is the sum of their speeds. That will be ...

(1800 m)/(30 s) = 60 m/s

When the cars are moving in the same direction, the speed at which one car laps the other will be the difference of their speeds. That will be ...

(1800 m)/(120 s) = 15 m/s

Sum and Difference

Now we know the sum and difference of speeds, we can find the speed (f) of the faster car to be ...

f + (f -15) = 60 . . . . . . . sum of speeds

2f = 75 . . . . . . . . . . add 15

f = 37.5 . . . . . . divide by 2

s = 37.5 -15 = 22.5 . . . . speed of slower car

The speeds of the cars are 22.5 m/s and 37.5 m/s.