<PRE><B>Question 225163</B>
It takes 4 hours for a boat to travel 56 miles downstream.
 The same boat can travel 36 miles upstream in 6 hours.
 Find the rate of speed of the boat in still water and the rate of the current.
:
let s = speed of the boat in still water
let r = rate of the current
Then
(s-r) = speed upstream
and
(s+r) = speed downstream
:
Write two distance equations: (dist = time * speed)
:
4(s + r) = 56
6(s - r) = 36
:
Simplify both equations, divide the 1st eq by 4, the 2nd eq by 6, results:
s + r = 14
s - r = 6
--------------addition eliminates r, find s
2s = 20
s = {{{20/2}}}
s = 10 mph in still water
and
s + r = 14
10 + r = 14
r = 14 - 10
r = 4 mph is the current
:
:
Check solution in original upstream equation
6(10 - 4) = 36
6(6) = 36
:
You can check it in the downstream equation</PRE>