Sunday, May 07, 2017

It's Sunny

     Get up.  Go outdoors.  I plan to -- you should, too.  This week will stay chilly and turn rainy, so I don't intend to waste a sunny day.

     Oh, here's a puzzle: My back yard is infested by Northern Creeper.  Every day, it doubles the area it covers.  If it can cover my whole yard in 48 days, how long would it take to cover half my yard?

     If a rake and a bag to pick all the creeper vines up and throw them away would have totaled $1.10 back in 1924 when Roseholme Cottage was built, and the rake cost a dollar more than the bag, what price was the bag?

     If it takes five rake-making machines five minutes to produce five rakes, how long would it take 100 rake-making machines to make 100 rakes?

     Get all three right and you're Sherlock Holmes.  I managed two off-the-cuff and vaporlocked on one; had to take it step-by-step to see where I went off the rails.

14 comments:

rickn8or said...

I was told there would be no math involved.

RandyGC said...

Word problems? Arrrgghhh! They should be more specific on the syllabus.

Ken said...

Think I got 'em, but for the sake of clarification: Can a single rake-making machine make a rake on its own, or is this an assembly line?

Divemedic said...

47 days, ten cents, and if each machine can make a rake on its own, 5 minutes. If it takes 5 machines in series to make a rake, then 25 minutes.

Murray Cuthbert said...

Diver nailed it.

I think!

Nicholas Krom said...

The bag would cost 5 cents.
x + (x + 1) = 1.10
2x + 1 = 1.10
2x = 0.10
x = 0.05

I agree with Divemedic's answers to the others.

Roberta X said...

Assume all rake-making machines are "spherical and identical," as the old logic joke puts it.

The rake-and-bag question is the worst for tripping you up. One right answer so far!

Bonus question, and my fave: if (on average) a hen-and-a-half lays an egg-and-a-half in a day-and-a-haf, how many eggs does the average hen lay in one day?

Aesop said...

Yeah.
47 days, 5 cents, and 5 minutes.

Aesop said...

And the bonus should be 2/3rds, or 0.66666666666666666etc.

waepnedmann said...

Mr. Spencer, the best math teacher in high school, (he made math interesting. He introduced us to Flatland and other thought provoking works) once proposed this problem to a group of his more...'ahem'...advanced students:

"If you took all of the male students in class and lined them up on the north side of the classroom and then lined up all the female students south side of the classroom. At a given signal each group would adavance halfway toward the middle line of the classroom.
How many repitions of movement would it require for the groups to come in contact with each other?
Answer: they would never come in contact, but would get close enough for all practical purposes.

He also performed an interesting survey: one day he asked all the students who were left handed to raise their hands. Half of the class were left handed. He commented that, across society, only one in seven people are left handed, but that in all the years he has been doing his non-scientific survey he has found that, in his upper division math classes, approximately 50% of the students are left handed.

I hope there are more teacher like him that survive the dumbing.

jetfxr69 said...

Without looking at others:
47 days, $0.05/a nickel, and 5 minutes...

Wolfman said...

I got them, and with a 4 year old spouting telephone numbers in my other ear, but I couldn't help but get distracted by 'Would Roundup kill that creeper? Because it is certainly going to come back' and 'I wonder how much of the yard was covered in creeper at the time of the raking, because that's gotta be a pretty generously outsized bag!'

Anonymous said...


The average hen lays one egg per day.

(I have no idea how often the average hen gets laid, however. Ask the hen in question. Her response will most likely be "Cluck you and the yummy omelette made with smokey bacon and cheese you rode in on.")

Anyways...

"If it takes five rake-making machines five minutes to produce five rakes, how long would it take 100 rake-making machines to make 100 rakes?"

Who put the run in the "Do run-run"?

fillyjonk said...

47 days, just like the wild blackberry in my backyard does.

(It doesn't even provide the consolation of tasty fruit. The berries are small, seedy, and flavorless. I should have guessed when I didn't see the birds eating them)