SOLUTION: The speed of a boat in still water is 15 mph. The Jacksons traveled 40 mi down the Woodset River in this boat in the same amount of time it took them to return 20 mi up the river.

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Question 1193557: The speed of a boat in still water is 15 mph. The Jacksons traveled 40 mi down the Woodset River in this boat in the same amount of time it took them to return 20 mi up the river. Find the rate of the river's current.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
The speed of a boat in still water is 15 mph. The Jacksons traveled 40 mi down the Woodset River
in this boat in the same amount of time it took them to return 20 mi up the river.
Find the rate of the river's current.
~~~~~~~~~~~~~~ 

Let c be the rate of current, in miles per hour.


Then effective rate with the current is 15+c mph,

while that against the current is 15-c mph.



The time traveling 20 miles against the current is    hours;

The time traveling 40 miles with    the current is    hours.



The times are the same, giving you this time equation

     = .



To find "c" from this equation, cross multiply


    20*(15+c)   = 40*(15-c)

    20*15 + 20c = 40*15 - 40c

    20c   + 40c = 40*15 - 20*15

       60c      =    300

         c      =    300/60 = 5.


ANSWER.  The rate of the current is 5 miles per hour.

Solved.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Here is a different method for solving this type of problem that I personally find easier than the traditional algebraic solution shown by the other tutor.

If x is the speed of the current, then the downstream speed is 15+x and the upstream speed is 15-x.

The upstream and downstream times are the same, and the downstream distance is 2 times the upstream distance. That means the downstream speed is 2 times the upstream speed:






ANSWER: The speed of the current is 5mph.
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