<p>You can't take the average of the two rates because they were for unequal times.</p>

<p>Your method would work if he ran up and down for the same amount of time. For example, if he ran up for 300 yards in 8 minutes and down for 500 yards in 8 minutes:</p>

<p>Rate = Total Distance / Total Time

= (800 yards)/(16 minutes)

= 50 yards/minute</p>

<p>With your method:

[(500/8) + (300/8)] / 2 = (62.5 + 37.5) /2 = 50 yards/minute</p>

<p>I can't explain it better than that the rates were not for equal times so you cannot just take an average. You have to add up the total distance and total time and use R = D/T.</p>