Joe start walking due north Bob starts waling due east When

Joe start walking due north, Bob starts waling due east. When they stop Bob has walked 1 mile further than Joe and they are 5 miles apart as the crow flies. How far did Bob walk?

Solution

Let\'s consider this problem geometrically. We\'ll call Joe\'s starting point J, Bob\'s starting point B and the point at which they meet we\'ll call M. The angle JMB is a right angle because Joe is walking north and Bob is walking east. We also know that the line from Joe\'s starting point to Bob\'s starting point is 5 miles. This line forms the hypotenuse of the right triangle JMB. We also know that the distance JM is one mile more than the distance MB.

Now let\'s collect these facts: