A man in a canoe in the middle of the river (somehow not moving yet) and a Person standing on the bank of the river are exactly the same distance...

A man in a canoe in the middle of the river (somehow not moving yet) and a Person standing on the bank of the river are exactly the same distance away from a pier down stream. The man in the canoe drops a bottle in the stream and it begins moving with the current of the river (Vc), at this same second both the person on the bank and the person in the canoe begin traveling towards the pier with velocity V0. (Keep in mind the V0 for the person on the bank is in relation to the ground while the v0 for the person in the canoe is in relation to the water. This makes the ground speed for the person on the bank Vo and the ground speed for the person in the canoe is V0+Vc). The two people start at the same location and finish when they have touched the pier, turned around, and reached the location of the bottle (which has moved down stream at a speed of Vc since the beginning)Who wins the race?

Let the distance of pier from starting point be ‘x’Case 1:The man in canoeTime to touch the pier, t1 = x/(vo + vc)During this time, bottle will be moved by distance = vc * t1Now, when the...