8. Let wvbe the speed of the wind and cvbe the speed of the car. (a) Suppose during time interval 1t, the car moves in the same direction as the wind. Then its effective speed is ,1effcwvvv=+, and the distance traveled is ,1 11()effcwdvt vvt==+. On the other hand, for the return trip during time interval t2, the car moves in the opposite direction of the wind and the effective speed would be ,2effcwv=−. The distance traveled is ,2 22effcw−. The two expressions can be rewritten as 12andcwddtt+=−=Adding the two equations and dividing by two, we obtain
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