You can
put this solution on YOUR website!Sam kayaked 3 miles downstream, then paddled back upstream to his starting place. If the total trip took 4 hours, and the current in the stream was 0.4 miles per hour, at what speed can Sam paddle his kayak in still water? (use the quadratic method to solve)
:
Let x = his speed in still water:
Then
(x+.4) = speed down-stream
(x-.4) = speed up-stream
:
Write a time equation: time = dist/speed
:
Time downstream + time up-stream = 4 hrs
+
= 4
:
Multiply equation by (x-.4)(x+.4) to get rid of the denominators
3(x-.4) + 3(x+.4) = 4(x+.4)(x-.4)
:
3x - 1.2 + 3x + 1.2 = 4(x^2 - .16)
:
6x = 4x^2 - .64
:
The quadratic equation:
4x^2 - 6x - .64 = 0
:
Use the quadratic formula: a=4; b=-6; c=-.64
:
:
:
:
:
; we only care about the positive solution here
:
:
x = 1.6 mph in still water
:
Check solution:
upstream: 1.6-.4 = 1.2
downstream: 1.6 + .4 = 2.0
+
=
1.5 + 2.5 = 4
