Question 542646: Please help me with this word problem, "a cargo ship travels for five hours with a current of 22 mph and then returns that same distance against the current in 8 hours. what is the ship's speed in calm water? how far did the boat travel one way?"
I did a rate times time equals distance table, but only know the times for both there are back, would 22 mph be the speed for the boat on the way there?
Thank you so much
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! "a cargo ship travels for five hours with a current of 22 mph and then returns that same distance against the current in 8 hours.
what is the ship's speed in calm water? how far did the boat travel one way?"
:
This is a poorly worded problem, they must mean that the boats effective speed with the current was 22 mph
A 22 mph current, although not unheard of, is pretty extreme.
:
Let s = ship's speed in calm water
Let c = rate of the current
then
s + c = 22 mph
or
c = (22-s); we can use this for substitution
:
Find the distance, dist = speed * time
22 * 5 = 110 miles one way
:
The distance equation for the trip against the current:
8(s-c) = 110
Replace c with (22-s)
8(s - (22-s)) = 110
8(s - 22 + s) = 110
8(2s-22) = 110
16s - 176 = 110
16s = 110 + 176
16s = 286
s = 286/16
s = 17.875 mph, which is a reasonable speed for a cargo ship
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