A.M. 12 total. Ran with the kids. Benjamin did 7, Jenny and Julia 3, Joseph 2, and Jacob 1. I was not planning on doing anything fast, but my legs were itching to go a little fast, and I had 7.4 miles left when I started the run with Benjamin, and I did not want run the extra 0.4 after I was done with him. So a natural solution was to run a short tempo starting about a mile before the turnaround, go a little further, then turn around and catch up. So I ran 1.25 up and 0.75 down. Benjamin ran the last 500 meters with me after I had caught up - I wanted to stop at some even number and I was already past 1.5 mark when I caught him. So I had these splits: uphill 88, 85, 87, 88 (5:48), 88, then turned around and went downhill - 82, 79, 76 (5:25, 11:13 for 2 miles). During the easy part of the run we had a physics lesson and talked about various forms of energy. If only our collision with the ground when running was perfectly elastic we could run forever with a very minimal effort and very little risk of injury. Instead our bones, muscles, and joints absorb the energy of the impact which could have been converted back into the energy of the movement. So a good portion of our hard work goes into pounding our body instead of moving forward. The harder you run, the greater fraction of the energy you lose. Reminds me of taxes.
P.M. William did 2x400 on the track by himself. I was originally going to run with him, but he insisted on doing it by himself. So he did the first one in 2:18, and the second in 2:34. Jacob did 1:39. Joseph did 1:27.