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### Like us? # Rate problem, two cars leave at the same time

Graph and then solve these equations by finding their point of intersection.

Q: Two cars leave at the same time. One car drives North at a rate of 65 m/hr and the other car drives south at a rate of 55 m/hr. In how many hours will the cars be 540 miles apart?

A: We will make use of the formula D=VT, where D=distance, V=velocity (speed) and T=time

Let Dn,Vn = Distance travelled by the north car, velocity of the north car
Ds, Vs = Distance travelled by the south car, velocity of the south car

The times they travel are the same, because they left at the same time. So tn=ts=t

We know that the two distances, Dn and Ds, add up to 540 miles:
Dn + Ds = 540

Now put in the formulas D=VT, instead of Dn and Ds, and solve for t:

Vn*t + Vs*t = 540
65t + 55t = 540
120t = 540
t = 4.5 hours

The cars will be 540 miles apart in 4.5 hours.