Hi Lanie.

Assume that both cars took the same route, so they went the same distance.

Remember that velocity (speed) is the distance divided by the time. So we can use algebra to solve this problem.

v = d / t.

In particular, let's call the two cars F and S (fast and slow). Then we can double up our equation with subscripts:

v_S = d_S / t_S

v_F = d_F / t_F

If we solve each of these for distance, we have:

d_S = v_S × t_S

d_F = v_F × t_F

But we said that both cars went the same distance, so d_S = d_F and so

v_S × t_S = v_F × t_F

Now look at the times involved. The fast car took 3 hours and the slow car took 3.5 hours, so we can substitute those into the equation:

v_S × (3.5) = v_F × (3)

And since we know the fast car's speed is 10 mph faster than the slow car, we know that v_F = v_S + 10, so we can substitute v_S + 10 in for v_F:

v_S × (3.5) = (v_S + 10) × (3)

Now, you can easily solve for v_S and the rest of the questions you are asked.

Cheers,
Stephen La Rocque.