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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
= = .
The only meaningful solution is the positive root r = = 1.796 miles per hour.
Answer. 1.796 mph for the slower boat and 7.796 mph for the faster boat.
Check. = 256.0 = 16^2. ! Correct !
Solved.
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Be aware !. The equation by @josgarithmetic from his post is W R O N G.
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O-o-o ! He just re-wrote it correctly from my post !