SOLUTION: The boat could sale at 5 times the speed of the current in the river thus the boat could go 84 miles upstream in 4 hours ‌more than it took to go 54 miles downstream. What was t

Algebra ->  Test -> SOLUTION: The boat could sale at 5 times the speed of the current in the river thus the boat could go 84 miles upstream in 4 hours ‌more than it took to go 54 miles downstream. What was t      Log On


   

Question 1151759: The boat could sale at 5 times the speed of the current in the river thus the boat could go 84 miles upstream in 4 hours ‌more than it took to go 54 miles downstream. What was the speed of the boat in still water?
Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x be the speed of the current, in miles per hour.


Then the speed of the boat in still water is 5x mph, according to the condition.



Then the effective speed of the boat upstream is (5x-x) = 4x mph.

The time to travel 84 miles upstream is  84%2F%284x%29  hours.



The effective speed of the boat downstream is (5x+x) = 6x mph.

The time to travel 54 miles downstream is  54%2F%286x%29  hours.


According to the condition

    84%2F%284x%29 - 54%2F%286x%29 = 4.


It is your time equation to find x.

Simplify it step by step


    21%2Fx - 9%2Fx = 4

    21 - 9 = 4x

    12     = 4x

     x     = 12/4 = 3.


Thus the speed of the current is 3 mph  and the speed of the boat in still water is 5*3 = 15 mph.    ANSWER

Solved.