Notices by Karen Campe (karencampe@mathstodon.xyz)

@alisonkiddle yes me too!! Been meaning to write a post along the lines of "what does the mean mean?"

@alisonkiddle love this (and yes very confusing for many students)

Must find out total distance divided by total time to get average speed, not just average the speeds.
Two methods:

Assume whole distance = 120 for ease of calculation, then each half of journey = 60
Distance = Rate • Time or D = RT
60 = 60 • T
1st part takes 1 hour
60 = 40 • T
2nd part takes 1.5 hours

Total distance = 120
Total time = 2.4 hours
Ave speed = 120/(5/2) = 240/5 = 48 mi/hr or 48 km/hr

@alisonkiddle
Second method!!
Notice that the harmonic mean of 60 and 40 is 5/120

\[ \frac{1}{60} +\frac{1}{40}= \frac{5}{120} \]

The answer to the average rate question is the reciprocal of half the harmonic mean.

\[ \frac{1}{2(\frac{1}{60}+\frac{1}{40}) }\]

\[ \frac{1}{\frac{5}{240 }}\]

Harmonic mean is a way to average rates.

When this was shown to me, I was amazed! It isn't usually taught to HS Ss in US Alg 2 when they see problems with rate of work.

@alisonkiddle ooh lovely!
{did not know there was a real place called Epping but do know the classic Genesis song "Battle of Epping Forest" 😉 hope you have no battles there today}