Mental math practice

A book runs 340 pages of roughly 300 words, and you read close to 250 words a minute.

About how many hours does it take to finish?

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The question you opened

Hours to finish the book

A book runs 340 pages of roughly 300 words, and you read close to 250 words a minute.

About how many hours does it take to finish?

about 6.8 hours

Three hundred and forty pages of 300 words is about 102,000 words. At 250 a minute that is 408 minutes, which is a little under 7 hours.

Three steps, each roundable. Pages times words per page gives 340 times 300, which is 102,000 words. Dividing by 250 words a minute gives 408 minutes. Dividing by 60 gives 6.8 hours. Rounding aggressively barely moves the answer. Call it 100,000 words and 250 a minute, and you get 400 minutes, so about 6.7 hours.

Call it 100,000 words and 240 a minute, which is 4 a second, and you get 417 minutes, close to 7 hours. Every route lands between six and a half and seven, and that band is the honest answer. The technique is to convert everything into a single unit before dividing anything. Mixing pages, words, minutes, and hours in one calculation is where estimates go wrong.

Words is the right unit here because both inputs are expressed in it, and minutes is the right unit for time because reading speed is quoted that way. Reading speed is the input that deserves scrutiny. Adult reading of ordinary prose typically falls somewhere between 200 and 300 words a minute, and technical material is far slower.

Since the estimate scales directly with that number, an answer of about seven hours is really an answer of between five and a half and eight and a half hours depending on the reader, and it is more useful to say so. The same three step conversion covers a great deal of planning. Rows times fields gives cells, cells over throughput gives seconds. Kilometres over speed gives hours. Units over rate gives time, every time, and the only skill is deciding which rate is realistic.

Technique: Round hard, then divide once

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