Question 363303: Traveling downstream, a boat can go 54 miles in 3 hours. Going upstream, it makes only half this distance in four times as long. What is the rate of the boat in still water, and what is the rate of the current?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Traveling downstream, a boat can go 54 miles in 3 hours.
Going upstream, it makes only half this distance in four times as long.
What is the rate of the boat in still water,
and what is the rate of the current?
:
Let s = boat rate in still water
Let c = rate of the current
then
(s+c) = effective speed downstream
and
(s-c) = effective speed upstream
:
Write a distance equation based on the statement (dist = time * rate):
"Traveling downstream, a boat can go 54 miles in 3 hours."
3(s+c) = 54
Simplify, divide both sides by 3
s + c = 18
s = (18-c); use this form for substitution
:
Write a distance equation based on the statement:
"Going upstream, it makes only half this distance in four times as long."
(Time: 4(3) = 12, half the distance 54/2 = 27 mi)
12(s-c) = 27
12s - 12c = 27
Substitute (18-c) for s
12(18-c) - 12c = 27
216 - 12c - 12c = 27
-24c = 27 - 216
-24c = -189
c = 
c = +7.875 mph is the current
then
s = 18 - 7.875
s = 10.125 mph is rate in still water
:
:
Check solution in the down stream equation
3(10.125 + 7.875) =
3(18) = 54
:
Confirm this in the upstream equation
12(10.125-7.875) =
12(2.25) = 27, half the distance
:
:
How about this, did it make sense to you?
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