You and your friend run outdoors at least 10 miles every day no matter what the weather (well almost). today the temperature is at a brisk 0 of with a -20 of wind chill. your friend, a real running fanatic, insists that it is ok to run. you agree to this madness as long as you both begin at your house and end the run at her nice warm house in a way that neither of you has to wait in the cold. you know that she runs at a very consistent pace with an average speed of 3.0 m/s, while your average speed is a consistent 4.0 m/s. your friend finishes warming up first so she can get a head start. the plan is that she will arrive at her house first so that she can unlock the door before you arrive. five minutes later, you notice that she dropped her keys. if she finishes her run first she will have to stand around in the cold and will not be happy. how far from your house will you be when you catch up to her if you leave immediately, run at your usual pace, and don't forget to take her keys?