SOLUTION: Nicholas paddles his canoe downstream from the Lodge to Bind Bend in 3 hours and then back upstream to the Lodge in 6 hours. If the distance from Lodge to Bend Bend is 15 miles, fi

Algebra ->  Finance -> SOLUTION: Nicholas paddles his canoe downstream from the Lodge to Bind Bend in 3 hours and then back upstream to the Lodge in 6 hours. If the distance from Lodge to Bend Bend is 15 miles, fi      Log On


   

Question 1087457: Nicholas paddles his canoe downstream from the Lodge to Bind Bend in 3 hours and then back upstream to the Lodge in 6 hours. If the distance from Lodge to Bend Bend is 15 miles, find Nicholas speed in still water and the speed of the current.
Answer by ikleyn(52825) About Me  (Show Source):
You can put this solution on YOUR website!
.
The effective speed of the canoe downstream is

15%2F3 = u + v    (1)

where u is the canoe speed in still water and v is the rate of the current.


The effective speed of the canoe upstream is 

15%2F6 = u - v    (2).

Simplify and re-write:

u + v = 5,      (3)
u - v = 2.5.    (4)


Now add the two equations. You will get

2u = 7.5  ---->  u = 7.5%2F2 = 3.75.


So the speed of the canoe in still water is 3.75 miles per hour.

Then the speed of the current, from (3), is

v = 5 - u = 5 - 3.75 = 1.35.


Answer. The speed of the canoe in still water is 3.75 miles per hour.

        The speed of the current is 1.25 miles per hour.

Solved.