Question

Two children who are bored while waiting for their flight at the airport decide to race from one end of the 20 m -long moving sidewalk to the other and back. Phillippe runs on the sidewalk at 2.0 m/s (relative to the sidewalk). Renee runs on the floor at 2.0 m/s . The sidewalk moves at 1.5 m/s relative to the floor. Both make the turn instantly with no loss of speed. How much time does it take the winner to win.

Answer 1

1.Renee:

$$t_1=t_2=\frac{20}{2}=10\ s$$

$$T_R=t_1+t_2=10+10=20\ s$$

2.Phillippe:

$$t_1'=\frac{20}{2+1.5}=5.7\ s$$

$$t_2'=\frac{20}{2-1.5}=40\ s$$

$$T_P=t_1'+t_2'=5.7+40=45.7\ s$$

3.Winner:

$$T=T_R=20\ s$$