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@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.