Alice, Bob and Charlie Math Problem

I ran across this on YT the other day.

It takes Alice and Bob 2 hours to do a task; Alice and Charlie 3 hours; and Bob and Charlie 4 hours. How long will it take for all three of them to do it?

It happens to tie in with something else I'm working on, so...

Almost everyone who didn't behave like a good pupil gave Alice and Bob the job. That way you pay four hours labour, but with three people, one of whom is all but useless by inspection, you're going to pay more than five and less than six hours. Or, Charlie would just get in the way and slow Alice and Bob down, which is pretty standard experience for anyone who has worked in teams.

To give the good pupil answer, you have to make a number of assumptions: a) you are not concerned with cost; b) three people can work together without getting in each other's way; c) the work rate of each person is not affected by a third person on the team. Since we are given no costs, we have to assume a). b) and c) have to be stated in the question, but are not.

I've always felt these questions are either a) posed by people who would not pass Logic 101, and/or b) are designed to see if you can make the "right" assumptions, in order to c) exclude awkward logical / lawyer-brained people who won't work well the Normies.

If you are going to use the good pupil assumptions, the correct reasoning starts by noticing that if you're going to "solve" for A, B, C, then those have to be the workrate (per hour) in order for the arithmetical operations to be meaningful.

Thus we get 1. a+b = ½ job / hr 

2. a+c = ⅓ job /hr 

3. b+c = ¼ job /hr

From which we get

4. b-c = 1/6 (eq 1- eq2) 

5. b = 5/24 (eq 3+eq 4, divided by 2) 

6. c = 1/24 (substitute 5 in eq 2) 

7. a = 7/24 (substitute 6 in eq 1)

so a+b+c = 13/24 (workrate / hr) time = 24/13 = 1.85 hrs.

Adding Charlie saves 9 mins, and costs a whole extra man-hour.

The math is fine, given the assumptions. it's the assumptions that are wonky.

If you have experience of the world.

If you're a high-school math problem-setter, you don't. So you make wonky assumptions.

Commenting on Current Affairs Means Letting Madness Take Up Space In Your Head

I've been finding it increasingly difficult to work up any enthusiasm for the foolishness of the world. You don't need me to tell you that the Ukraine War is awful, that Woke is a blight on the land, that the economy is a mess, and that anyone under forty has to be treated with kid gloves (vegan fake kid gloves, of course) lest they "call you out" for wrongthink.

The problem with commenting, especially political and economic commentary, is that you're always living someone else's life.

You expend a lot of thought and concentration on describing, interpreting and drawing the possible consequences of what other people are doing.

You're letting other people's madness take up space in your head.

I'm pretty darn sure I don't want that anymore. I hardly noticed when I had a day job, because day jobs are all about dealing with other people's madness, so it was more of the same.

I notice the madness of the things I comment on now I don't have a day job.

I think I want out.

Can You See The Mighty A2, The Famous Roman Road, In This Picture?

 

The A2 is that big ol' road that's full of lorries waiting to get onto ferries at Dover. Three lanes, backed up for five miles, and that's on a good day. It's one of the great importing roads in this country and therefore in the world, the UK having the fifth largest economy in the world.

It was based on the Roman road from Londinium to Doverum (or whatever they called it, I'm sure Wikipedia has the proper answer). So that makes it pretty important at the London end as well.

Can you see it in this picture?

Yep. On the right. No barriers, no signs, barely any traffic and this was mid-day Thursday.

This is what the A2 looks like at Blackheath, just outside the walls of Greenwich Park.

I wonder if this happens to other famous roads in other countries?

Barking Riverside

Everyone should visit Barking Riverside by boat. The ride down goes past all the fancy skyscrapers and riverside flats of Docklands, passes the O2 at North Greenwich and then after a couple minutes more of smaller riverside flats on the south bank... you're in the wide open river with nothing higher than the flight of a seagull to your left or right. The flatlands of Essex and Kent. I'll have some pictures of that later. Barking Riverside is in the middle of nowhere, literally, and yet less than, what? five miles from Docklands?

 

The View Upriver From North Greenwich

This is the view from the Uber Boat heading downriver (and so looking upriver from the back) across the North Greenwich peninsula and across the Isle of Dogs, which is where most of 'Docklands' is. 

I was working in 'Docklands' when Canary Wharf was being built, and most of the buildings in this photograph were not even the dreams of developers. Where did all these buildings come from? More to the point, where do the people come from to pay the rents or mortgages (residential) or sit at desks that companies are paying rent on. 

I'm never really going to believe it's all real, no matter how many times I visit the place.

Thirteen Years of Blogging: 2009 - 2022

The first post on this blog is dated 29th April 2009.

That's thirteen years. Which is pretty good going for a personal blog.

A while ago, one of my rare commenters remarked that this blog seemed to be mostly about me getting things off my chest.

Fair comment.

I think that's why I started doing it.

I'm certainly not in it for the money.

Every now and then I wonder about being more professional about the whole thing.

Being more professional would require that I choose a subject and offer a consistent view of the world around that subject.

I would have to produce content for the clicks.

I'd start caring about views and engagement.

I'd have to do SEO (which I think is voodoo anyway) and other such stuff.

The financial and personal reward for all that would be?

Zip. Nada.

Sounds like a decision to me.

Moody Soho Cafe Interior Photograph

 

It's been a long time since I took photographs from inside a cafe. It's taking a while to get back into using a proper camera and not being self-conscious about it. This was one afternoon in the Caffe Nero on Old Compton Street.