Question 694164
Since Jane is due north and Juan is due east they are moving at right angles to each other.
So Pythagoras theorem has to be applied.

at a given time jane is 3 miles from home

Let Juan be x miles from home

they are at a distance of (x+1) miles 

the two legs are 3 & x

The hypotenuse is (x+1)

x^2+3^2=(x+!)^2

x^2+9= x^2+2x+1

x^2 cancels off

9=2x+1
2x=9-1
2x=8
/2
x= 4

Juan is 4 miles from home