Question 699652: Please help me! I need to solve this word problem using the eliminating method.
A steamboaat went 8 miles upstream in 1 hour. The return trip took only 30 minuts. Assume that the speed of the current and the direction were constant during both parts of the trip. Find the speed of the boat in still water and the speed of the current.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A steamboat went 8 miles upstream in 1 hour.
The return trip took only 30 minutes.
Assume that the speed of the current and the direction were constant during both parts of the trip.
Find the speed of the boat in still water and the speed of the current.
:
Let s = the boat speed in still water
Let c = the rate of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
Change 30 min to .5 hr
Write a distance equation for each way, dist = time * speed
1(s-c) = 8
.5(s+c) = 8
:
The 1st equation we can ignore the 1,
the second equation divide both sides by .5
s - c = 8
s + c = 16
--------------adding eliminates c, find s
2s = 24
s = 12 mph in still water
:
find c
12 + c = 16
c = 16-12
c = 4 mph is the current
:
:
:
Check this
1(12 - 4) = 8
and
.5(12 + 4) = 8
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