1. ## Averages & Manuscripts

Mother asked Vera to type a manuscript. Vera declared: "I will type an average of 20 pages a day."
She typed the first half of the manuscript rather lazily, at 10 pages a day. To make up for it, she typed the second half at 30 pages a day.
"See, I did average 20 pages a day." Vera concluded. "Half of 10 + 30 is 20."
"No, you didn't," her mother said.
Who was right?

2. ## Re: Averages & Manuscripts

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Her mother is. She averaged 15 pages /day

Say P is number of pages
She did 0.5*P pages in 0.5*p/10 days
and she did 0.5*P pages in 0.5P/30 days

Total Pages / day = P/(0.5*P/10 +0.5*P/30)
Total Pages / day = 30P/(3*0.5*P +0.5*P)
Total Pages / day = 30/(1.5+0.5) = 30/2 = 15 pg /day</font color=yellow></span hi>

Steve

3. ## Re: Averages & Manuscripts

<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>If she typed the manuscript in 2 halves at the two different rates, as described, she must have spent 3 times as long typing at 10ppd as she did typing at 30ppd. Her average speed is the weighted mean, given by:
(3n x 10 + 1n x 30)/(n + 3n) = 15ppd where n is number of days typing at 30ppd
Mother still knows best apparently.</font color=yellow></span hi>

Alan

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