Question 1130701
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<pre>
If the speed of the slower boat is  "r"  miles per hour, then the speed of the faster boat is  (r+6) miles per hour.


You have the right angle triangle with the legs  2r  and  2*(r+6)  miles.

The hypotenuse is 16 miles, which gives you an equation


(2r)^2 + (2*(r+6))^2 = 16^2


4r^2 + 4r^2 + 48 r + 144 = 256


8r^2 + 48r - 112 = 0

r^2 + 6r - 14 = 0


{{{r[1,2]}}} = {{{(-6 +- sqrt(6^2 + 4*14))/2}}} = {{{(-6 +- 9.592)/2}}}.


The only meaningful solution is the positive root  r = {{{(-6 + 9.592)/2}}} = 1.796 miles per hour.


<U>Answer</U>.  1.796 mph for the slower boat and  7.796 mph for the faster boat.


<U>Check</U>.   {{{(2*1796)^2 + (2*7.796)^2}}} = 256.0 = 16^2.    ! Correct !
</pre>

Solved.


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<U>Be aware !</U>.  &nbsp;&nbsp;The equation  &nbsp;&nbsp;{{{r^2+(r+6)^2=16^2}}}  &nbsp;&nbsp;by &nbsp;@josgarithmetic from his post is &nbsp;&nbsp;<U>W R O N G</U>.



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O-o-o ! He just re-wrote it correctly from my post !