Question 154886: A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.
Answer by orca(409)   (Show Source):
You can put this solution on YOUR website! Let x be the speed of the boat in still water.
Let y be the speed of the current of the river.
Then
the boat's downstream speed relative to the river bank is x + y,
the boat's upstream speed relative to the river bank is x - y.
As the boat travels 48 miles downstream in 3 hours, we have
3(x+y)=48 ...............(1)
As the boat travels 48 miles upstream in 6 hours, we have
6(x-y)=48 ................(2)
Simplifying equation (1) and (2) by dividing them by 3 and 6 respectively, we have
x+y=16 ........(3)
x-y=8 ........(4)
Adding (3) and (4) together, we have
2x = 24
So x = 12
Substituting x = 12 into (3), we obtain
12 + y = 16
Solving for y, we get
y = 4
So the speed of the river is 4 miles per hour.
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