Two boats leave same point same time. One boat east other north. One 6 kilometer faster. After 4 hours, the boats are 67 kilometers apart.

Question

Let x be speed of the slower boat. Write a quadratic equation that models the situation.

Answer 1

Draw the right triangle with rt angle at Origin, northbound leg labeled 4x (distance = 4 hours times x km/hr)

and the eastbound leg labeled 4(x+6).

 

Label the hypotenuse 67.

 

By Pythagorean theorem, the square of the northbound leg + the square of the eastbound leg = 67 squared.

 

This is the desired quadratic equation.  You can simplify it if you like;

remember that the square of (x+6) is x² + 12x + 36