Question

Rosa works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 55 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

Ray's distance from Home = 1512 miles

Explanation:

In the question,

Let us say,

The position of their house is at O.

So,

The work place of Rosa is at, say, A.

The work place of Ray is at, say, B.

So,

When distance of Rosa was 55 miles from Home (O).

Then,

CD = (x + 1) miles

OD = x miles

So,

Using the Pythagoras Theorem, in triangle COD,

`CD^(2)=CO^(2)+DO^(2)\\(x+1)^(2)=55^(2)+x^(2)\\x^(2)+1+2x=3025+x^(2)\\2x=3024\\x=1512\,miles`

Therefore, the distance of Ray from Home is given by,

OD = 1512 miles