Question

Two boats travel at right angles to each other after leaving the same dock at the same time. one hour​ later, the boats are 25 miles apart. if one boat travels 17 miles per hour faster than the other​ boat, find the rate of each boat

Answer 1

The speed of the two boats are 7 miles per hour and 24 miles per hour.

Step-by-step 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)`

`2x^(2) +34x + 289=625`

`2x^(2) +34x - 336=0`

`(x+24)(x-7)=0`

∴ 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.