Let $x$ be the speed of the southbound boat in miles per hour. Then the eastbound boat has speed $x + 1$ miles per hour. After 5 hours, the southbound boat travels $5x$ miles and the eastbound boat travels $5(x + 1)$ miles. Therefore, by the Pythagorean Theorem,
\[25^2 = (5x)^2 + (5(x + 1))^2.\]Simplifying the expression on the right, we find
\[625 = 25x^2 + 25(x^2 + 2x + 1).\]This simplifies to $50x^2 + 50x - 600 = 0.$ Dividing by 50, we get $x^2 + x - 12 = 0,$ which factors as $(x - 3)(x + 4) = 0.$ Hence, $x = \boxed{3}.$
Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 1 mi/h faster than the southbound boat. After 5 h the boats are 25 mi apart. Find the speed of the southbound boat.
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