In a race over 4 km Ryan ran at a constant speed. Sophie, however, ran the first 2 km at a speed 1 km/h more than Ryan and ran the second 2 km at a speed 1 km/h less than Ryan.

Question

In a race over 4 km Ryan ran at a constant speed. Sophie, however, ran the first 2 km at a speed 1 km/h more than Ryan and ran the second 2 km at a speed 1 km/h less than Ryan.
Who won the race?

Steve · Answer

If Ryan's speed was r, then since time = distance/speed, compare 4/r and 2/(r-1)+2/(r+1) This is easy, since it just involves comparing 4r/r^2 and 4r/(r^2-1)