Question 837126: A kayaking group with a guide travels 16 miles downstream, stops for a meal, then travels 16 miles upstream. The speed of the current remains constant throughout the trip. Find the speed of the kayak in still water.
leave...10am
stop for meal...12 noon
return...1pm
finish...5pm
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A kayaking group with a guide travels 16 miles downstream, stops for a meal, then travels 16 miles upstream.
The speed of the current remains constant throughout the trip.
Find the speed of the kayak in still water.
leave...10am
stop for meal...12 noon
return...1pm
finish...5pm
:
Let s = speed in still water
Let c = rate of the current
then
(s+c) = effective speed down stream
and
(s-c) = effective speed upstream
:
From the given information, we know travel time downstream is 2 hrs and
the travel time upstream is 4 hrs
:
Write a distance equation for each way; dist = time * effective speed
2(s+c) = 16
4(s-c) = 16
Simplify, divide the 1st equation by 2, divide the 2nd equation by 4
s + c = 8
s - c = 4
-----------Adding eliminates c, find s
2s = 12
s = 12/2
s = 6 mph in still water
:
:
Confirm this solution; find the current
6 + c = 8
c = 2 mph is the current
Find distances with these values
2(6+2) = 16
4(6-2) = 16
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