Answer
Tom is going 17 mph, and Celia is going 20 mph.
Work Step by Step
Recall that velocity is equal to change in distance over change in time. We call t the time it takes Tom. Thus, we obtain:
$\frac{60}{t-2} = \frac{ 85}{t} +3 $
We create common denominators and solve for t:
$ \frac{60t}{t(t-2)} = \frac{85(t-2)}{t(t-2)} + \frac{3t(t-2)}{t(t-2)}$
Since the denominators are the same, we cancel them out and solve. (Recall, t cannot be negative.)
$60t = 85t-170 + 3t^2 -6t \\ 3t^2 +19t - 170 = 0 \\ (t-5)(3t+4) = 0 \\t=5$
Thus, for Tom:
$ v = 85/5 = 17$ mph
Since Celia was 3 mph faster, she went 20 mph.
