Thursday, June 3, 2010

Genie and Hitch

Suppose Genie walks her dog Hitch on a trail where Hitch can run around without a leash. Genie wants to make sure Hitch gets a certain number of miles of running per day, but she doesn't want to walk that far herself. How long does Genie have to walk to make sure Hitch gets enough running?

The first step to solving most problems is to figure out what you know, and what you are trying to find out. Writting things down is always a good idea. Trying to keep it all in your head just makes things harder.

For Genie to figure out how far she needs to walk, she's going to have to make some estimates or measurements. She wants to know how fast Hitch is running so that she'll know how far he runs fur the duration of the walk. Let's say Genie estimates Hitch's running speed to be twice as fast as her walking speed. So if Genie walks at X mph, Hitch runs at 2X mph. In time T, Genie walks T*X miles, and Hitch runs T*2X miles. In comparing those distances, we see that Hitch runs twice as far (2XT) as Genie walks (XT). That means, Genie only needs to walk half the distance she wants Hitch to cover.