SOLUTION: 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 are constant during both parts of the tr

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Question 159038: 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 are constant during both parts of the trip. Find the speed of the boat and still water and the speed of the current.
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of the boat in still water
And let x=speed of the current
Distance upstream=(r-x)*1=8 (upstream we subtract the speed of the current)
Distance downstream=(r+x)*0.5=8 (downstream we add speed of current)
So we now have:
r-x=8-------------------------------eq1
0.5r+0.5x=8------------------------------eq2
Multiply eq2 by 2 (and we get r+x=16) and then add eq1 and eq2:
2r=24 divide each side by 2
r=12 mph--------------------------speed of the boat in still water
substitute r=12 into eq1:
12-x=8 subtract 12 from each side
12-12-x=8-12 collect like terms
-x=-4 divide each tide by -4
x=4 mph-------------------speed of current
CK
8=(12-4)*1
8=8
and
8=(12+4)*0.5
8=8
Hope this helps----ptaylor