Question 190306: A cruise boat travels 60 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.
Answer by orca(409)   (Show Source):
You can put this solution on YOUR website! Let x represent the speed of the boat in still water.
Let y represent the speed of the stream.
Then
the speed of the boat downstream = x + y
the speed of the boat upstream = x - y
Since the boat travels 60 miles downstream in 3 hours, we can write the first equation as:
3(x+y) = 60 .....................(1)
Since the boat returns to its starting point upstream in 12 hours, we can write the second equation as:
12(x-y) = 60 .....................(2)
After simplifying , equations (1) and (2) becomes:
x + y = 20 ................(3)
x - y = 5 ................(4)
Adding up (3) and (4), we have
x + y + x - y = 20 + 5
2x = 25
x = 12.5
Substitute x = 12.5 into equation (3), we have
12.5 + y = 20
Solving y, we have
y = 20 - 12.5
y = 7.5
So the speed of the stream is 7.5 miles per hour.
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