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?

Givens:

2 cars

Travel distance 1800 meters

Variables and Definitions:

Velocity(V) is speed in meters/second (m/s)

Time(t) is in seconds (s)

a)Find the speed of the cars if they travel in opposite directions on the track and pass each other every 30 seconds.

Since the cars are traveling opposite each other, we add their speeds. In 30 seconds the two cars together travel 1800 meters

30s(V1m/s+V2m/s)=1800m (note: I divide both sides by 30 because we want the speeds, not distances)

So we have one equation with 2 unknowns

(Eq. 1)V1+V2 = 60

b) Find the speed of the cars if they travel in the same direction on the track and pass each other every 120 seconds.

Since the cars are travel the same direction, we subtract their speeds. In 120 seconds the difference in distance travelled = 1800 meters.

120s(V1m/s-V2m/s) = 1800

We now have a second equation with 2 unknowns:

(Eq. 2) V1-V2=15

To find V1 and V2 we need to solve the system of the two equations, 1 and 2.

V1+V2=60

V1-V2=15

If we add these two equations we get: 2V1=75, so V1=37.5. Straighforward substitution is all it takes to find V2.

V1=37.5m, V2=22.5m

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