mary works due north of home Her husband Juan works due east

mary works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Mary is 3 miles from home, the distance between them is one mile more than Juan\'s distance from home. How far from home is Juan?

Solution

Let Juan\'s distnace from home be x miles

Now distance between Juan and Mary = 1+x

Now since Mary heads north and Juan east

They form a rt angled triangle with hypotenuse = (1+x)

So, 3^2 +x^2 = (1+x)^2

Solve: 9 + x^2 = 1+x^2 +2x

9-1 = 2x

x=4

Juan is x = 8/2 = 4 miles from home