Expert: Steve Holleran - 9/12/2007

Question
A girl paddles her kayak upstream from her home to her friends home, taking 2.5 hours for the journey. She returns that afternoon in 1.5 hours. If the river is flowing at 2.5km/h, find:
i/her paddling speed in still water.
ii/the distance to her friend's place.

Answer
Hi Nuri,

Okay, lets let her rowing speed in still water = x.

Then upstream her speed is (x - 2.5)
    downstream her speed is (x + 2.5)

Now use D = R * T in each case:

Upstream:            D = (x - 2.5)(2.5)

Downstream:          D = (x + 2.5)(1.5)

Since the distance up and down is the same, set these = :

         (x - 2.5)(2.5) = (x + 2.5)(1.5)

           2.5 x - 6.25 = 1.5x + 3.75

                     1x = 10   so her speed is 10 km/hr.

Then downstream, D = (10 + 2.5)(1.5) = 12.5 * 1.5 = 18.75 Km

Hope this helps you out.

Steve Holleran