Piecewise function story problem

Question

At a recent softball game, Bill hit a double. He ran from home to second base (a distance of 120 feet) at a speed of 20 feet/sec. The next batter was up to bat for 1 minute but popped up to the pitcher, so Bill did not go anywhere. The third batter hit the first pitch over the fence for a homerun, so Bill was able to jog home (a distance of 120 feet) at a speed of 10 feet/sec. Write a piecewise function for the distance Bill traveled as a function of time in seconds.

Answer 1

Let t: time (sec)

d(t): total distance Bill has traveled (ft)

d(t) = { 20t ; 0 ≤ t ≤ 6

120 ; 6 < t ≤ 66

120 + 10 (t - 66) ; 66 < t ≤ 78