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.

Algebra ->  Equations -> 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.      Log On


   

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) About Me  (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
:
16%2F%28%28s-c%29%29 + 24%2F%28%28s%2Bc%29%29 = 6
and
12%2F%28%28s-c%29%29 + 36%2F%28%28s%2Bc%29%29 = 6
Simplify both equations, divide the 1st by 2, the 2nd by 3 and we have
8%2F%28%28s-c%29%29 + 12%2F%28%28s%2Bc%29%29 = 3
4%2F%28%28s-c%29%29 + 12%2F%28%28s%2Bc%29%29 = 2
----------------------------------------Subtraction eliminates (s+c)
4%2F%28%28s-c%29%29 + 0 = 1
4 = s - c
(c+4) = s
Using the first original equation replace s with (c+4)
16%2F%28%28%28c%2B4%29-c%29%29 + 24%2F%28%28%28c%2B4%29%2Bc%29%29 = 6
16%2F4 + 24%2F%28%282c%2B4%29%29 = 6
4 + 24%2F%28%282c%2B4%29%29 = 6
24%2F%28%282c%2B4%29%29 = 6 - 4
24%2F%28%282c%2B4%29%29 = 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
12%2F4%29 + 36%2F12 = 6
3 + 3 = 6