Suppose That Celia Rides Her Bicycle 60 Miles In 2 Hours Less Time Than It Takes Tom To Ride His Bicycle 85 Miles. If Celia Rides 3 Miles Per Hour Faster Than Tom, Find Their Respective Rates?

Let c represent Celia's speed. Then c-3 is Tom's speed. The equation for the travel times is
  60/c + 2 = 85/(c-3)
Multiplying both sides of this equation by c(c-3), we get
  60(c-3) + 2c(c-3) = 85c
Subtracting 85c from both sides, we get
  2c^2 -31c - 180 = 0
  2c^2 -40c + 9c - 180 = 0    (we choose to rewrite -31c so we can find the factors easier)
  2c(c-20) + 9(c-20) = 0    (first stage of factoring)
  (2c+9)(c-20) = 0    (second stage of factoring)
  c = -9/2  or  c = 20    (values of c that make the factors equal to zero. We choose the positive answer.)

Celia rode 20 miles per hour, Tom rode 17 miles per hour.

Check
  Celia's time was 60 mi/(20 mi/hr) = 3 hr
  Tom's time was 85 mi/(17 mi/hr) = 5 hr, which is 2 hours longer than Celia's time.