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,
[tex] x^{2} +(x+17)^{2}=25^{2} [/tex]
[tex] 2x^{2} +34x + 289=625 [/tex]
[tex] 2x^{2} +34x - 336=0 [/tex]
[tex] (x+24)(x-7)=0 [/tex]
∴ 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.
