How far from home is Ray?

Question

Fran works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Fran is 7 miles from home, the distance between them is one mile more than Ray's distance from home. How far from home is Ray?

Answer 1

Draw and label a diagram.

d is Rays' distance from home

d + 1 is Fran's distance to Ray

7 is Fran's distance from home

This forms a right triangle.

(x + 1)² = 7² + x²

 

Can you solve for x and answer?

Answer 2

 

They start at the origin(0,0)

 

Fran goes north (positive y-axis)

Ray goes east (positive x-axis)

 

 The right triangle has  leg measure 7 per Fran.

 The hypotenuse is the distance between them.

 Y is the distance Ray has traveled.

 

 So the hypotenuse is 1 more than Y based on the given information.

 Then the hypotenuse is Y+1

 

7^2 + Y^2 = (Y+1)^2

 

49 + y^2 = y^2 + 2y + 1

 

49 = 2y + 1

 

48 = 2y

 

y=24

 

Check: 7^2 + 24 ^2 = 49 + 576 = 625 = 25^2 is a known pythagorean triple

Ray is 24 miles from home.

The distance between them is 25 miles.