2 cars with different speeds travelling 2 m

Question

Given two toy cars with different speeds, and a finish line that is 2.0 m from the start, how much farther back does the faster of the two cars have to be placed so that the two cars will cross the finish line at the same time, if they are started at the same time.

How would I go about solving this problem

Find the speed of each car. Time how long each car travels 2 meters use v=d/t to find speed. Once I have speed then what?

Answer 1

The speeds of the cars are not given, but the distance from starting line to finish line is 2 m.

If both cars start at the same time and finish at the same time, we can write the time equations as

t_fast = D +X / V_fast and t_slow = X / V_slow where t is time, V is velocity, D is distance of 2 m and X is the distance the faster car should be behind the starting line.

We know that t_fast = t_slow so D + X / V_fast = D / V_slow.

Assuming we know the speeds of each car, we can solve for X which is what is needed.