SOLUTION: a boat goes 16 km upstream and 24 km downstream in 6 hours. it also covers 12 km upstream and 36 km downstream in same time. find the rate of speed still in water and stream.

Question 880014: a boat goes 16 km upstream and 24 km downstream in 6 hours. it also covers 12 km upstream and 36 km downstream in same time. find the rate of speed still in water and stream.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a boat goes 16 km upstream and 24 km downstream in 6 hours.
it also covers 12 km upstream and 36 km downstream in same time.
find the rate of speed still in water and stream.
:
Let s = rate of speed in still water
let c = rate of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Write a time equation for each trip, time = dist/speed
:
+ = 6
and
+ = 6
Simplify both equations, divide the 1st by 2, the 2nd by 3 and we have
+ = 3
+ = 2
----------------------------------------Subtraction eliminates (s+c)
+ 0 = 1
4 = s - c
(c+4) = s
Using the first original equation replace s with (c+4)
+ = 6
+ = 6
4 + = 6
= 6 - 4
= 2
24 = 2(2c + 4)
24 = 4c + 8
24 - 8 = 4c
c = 16/4
c = 4 mph is the rate of the stream
and
s = c+4
s = 4 + 4
s = 8 mph is the rate in still water
:
:
See if that checks out in the 2nd equation
+ = 6
3 + 3 = 6

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