Why Units Matter

So I was reading through an arithmetic textbook at the library yesterday, and found a section where some reader had crossed out the word "weeks" several times and replaced it with "days."

Here's why units matter in a math problem.

Suppose 12 men can mow 480 acres in 56 weeks. Note: there are only 52 weeks in a year.

If you do the math, that means 1 man can do 40 acres in 56 weeks, or 1 acre in 1.4 weeks. That means he's doing about 1/10 of an acre a day. What is he mowing with - his wife's sewing scissors??

Now suppose 12 men can mow 480 acres in 56 days. 56 days is 8 weeks, but we'll only work 6 out of 7 days a week (Sundays, gang, can't work on a Sunday) which means really we're only working 48 of those 56 days. So 1 man can do 40 acres in 48 days, which is starting to look like about an acre a day.

Doesn't that look a lot better? Especially since the acre used to be defined as how much a man could plow (which, yes, is a little different from mowing) in a day!

Units matter. And that's my math geekiness for the day.

Research accomplished Friday:

1) Read a bunch of arithmetic books

2) Read a bunch of almanacs

3) Discovered that "Beware the Cat" was an early modern book about talking cats.

4) Decided to call it quits early when I started putting almanacs into the wrong folders and writing about "bencil parks" in my manuscripts.

Have a great weekend!