How many hours does it take for you and the bobber to meet?

Question

You can paddle your canoe seven miles per hour through any placid lake. The stream flows at three miles per hour. The moment you start to paddle up stream a fisherman looses one of his bobbers in the water fourteen miles up stream of you.

How many hours does it take for you and the bobber to meet?

Answer 1

The speed of the canoe at resting stream is 7 MPH.
The stream speed is 3 MPH and since the canoe is going upstream the effective velocity it has is 7 - 3 = 4 MPH.
Now after he started paddling the bobber started coming towards the canoe from 14 miles away at the speed of the stream ie., 3 MPH.

To simplify the situation we can add the velocity of the bobber to that of the effective velocity of the canoe which is 4MPH making its velocity equal to 7 MPH and the velocity bobber can be reduced to 0 MPH. This simplification is valid because in both the cases the relative velocity between the 2 is the same but the simplified case has the added benefit of simple calculations.

Now since effective velocity of the canoe is 7 MPH and the distance to bobber is 14 miles, the time taken will be
14/7 = 2 hours.