Question 1174765
<br>
Using formal algebra....<br>
Let x be her speed in still water.<br>
Then her upstream speed is x-4; her upstream time (distance divided by speed) is 65/(x-4).
And her downstream speed is x+4; her downstream time is 65/(x+4).<br>
The total time is 18 hours:<br>
{{{65/(x-4)+65/(x+4) = 18}}}<br>
Multiply through by (x-4)(x+4) to get a quadratic equation that can be solved to find the solution.<br>
Knowing how to solve the problem using formal algebra is good.  But you can get to the answer much faster -- and get a lot more good mental exercise -- by solving it using logical reasoning and simple arithmetic.<br>
Since the total time is (exactly) 18 hours, the times for the two legs of the trip are probably whole numbers of hours.<br>
The difference between the upstream and downstream speeds is 8 mph.  So we need to find two numbers whose difference is 8 that both divide evenly into 65.<br>
But 65 is 5*13; and the difference between 5 and 13 is 8.<br>
So suppose the upstream speed is 5 mph and the downstream speed is 13 mph; that makes her speed in still water 9 mph.  And her time upstream is 65/5 = 13 hours, and her time downstream is 65/13 = 5 hours -- making the total time 18 hours, which is what we needed.<br>
ANSWER: Her speed in still water is 9 mph.<br>