The speed of the two boats are 7 miles per hour and 24 miles per hour.
Explanation:
Let the speed of the first boat be x miles per hour and second boat be x+17 miles per hour.
As they move at right angle to each other, this problem can be solved using Pythagoras theorem.
The two boats will form a right angle with hypotenuse 25 miles after one hour.
Applying the theorem we get,
![x^{2} +(x+17)^{2}=25^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%28x%2B17%29%5E%7B2%7D%3D25%5E%7B2%7D%20%20%20)
![2x^{2} +34x + 289=625](https://tex.z-dn.net/?f=%202x%5E%7B2%7D%20%2B34x%20%2B%20289%3D625%20)
![2x^{2} +34x - 336=0](https://tex.z-dn.net/?f=%202x%5E%7B2%7D%20%2B34x%20-%20336%3D0%20)
![(x+24)(x-7)=0](https://tex.z-dn.net/?f=%20%28x%2B24%29%28x-7%29%3D0%20)
∴ x= -24 and 7
As speed cannot be negative,
We get speed of first boat = 7 miles per hour and
Speed of second boat = 7+17 = 24 miles per hour.