Work it out with a pencil

L-19
The exam season is once more upon us.

Read the following statement and answer the questions:

'British Waterways has reduced the price of self-pumpouts from £12.10 to £10. "We will recalibrate our meters to collect 25 instead of 30 units from each pre-payment card" said Sally Ash, Head of Boating Development at a national boating issues meeting'
(Waterways World, June 2007, p. 47)

a) How many partly used pre-payment cards will you need to collect before you can use them for a pumpout?

b) A pumpout lasts six minutes. How frequently will you have to insert a card with five units of credit on it to take advantage of this?

c) If 30 units cost £12.10, what is the cost of
i) 5 units
ii) 1 unit
iii) a Porta-Potti

d) Just before the cost of a pumpout doubled, Sarah bought ten pre-payment cards.
i) How much did she think she had saved?
ii) How much has she actually saved?

You may use a slide rule.

Just as (as I once mentioned) I may be one of the youngest people in the country who can darn, I must also have been among the last to have been taught to use a slide rule. Why, I have no idea, as we did already, by then, have primitive electronic calculators, but I suppose they thought it was good for us, like spinach, and Latin (which sadly I didn't get to do). Everyone else in the class had a new, white plastic slide rule from the school shop. I had my father's old army one, Gnr Hale inscribed on it in ink; it was made of wood and the sliding bit used to stick (while the cursor, celluloid in a metal frame, used to fall off and get lost). While other people were reading off their answers, I was still trying to wriggle it by minute degrees into place.

I'm sure I could have had a new one if I'd wanted; I was probably just being deliberately perverse. I hated maths. I also hated woodwork, metalwork, needlework and PE, but maths was daily misery and torture. In this I was a grave disappointment to my mother, whose two academic passions were Latin and mathematics. Not having the opportunity to do the former, I also had no aptitude whatever for the latter. Night after night she would try to help/encourage/coax/bully/berate me - sometimes with us both ending up in tears, but more often just me - over my School Mathematics Project textbooks. It worked, up to a point; I scraped a C at O Level.

My friend Sally, whom I sat next to while gradually working a hole through the desk with my compass (do you know they don't even have proper pointed compasses any more? Truly, the world is going to the dogs) however, got a D, in the days when that was unequivocally a Fail, and had to retake her maths O Level at sixth form - where she promptly got an A. I draw from this (and the fact that I like symbolic logic) the comforting conclusion that I wasn't really that bad but we must just have had a dreadful teacher.

My mother so liked maths that once she bought me a little book about algebra and got so engrossed in it on the way home that she missed her bus stop. To me, of course, algebra was another impenetrable mystery. Only once, many years later while going over something with Baz, it suddenly fell into place; for one fleeting, marvellous moment I could see it; it was like alchemy, and then just as suddenly it was gone again.

And talking of pumpouts, some time soon we have to face up to this unsavoury little topic in relation to Warrior. Owing to an organisational oversight, our engine was removed before we'd got round to emptying said tank. Oh well, we thought, in for a penny (as it were) and carried on using it with gay abandon until we could do so no more, at which point we firmly closed the lid and tried to ignore it, just occasionally slinging a slug of blue into the bowl. No, it doesn't smell (or if it does we've become completely inured to it) but we do wonder what sort of a job we have on our hands (oh god, it's impossible to write this without turning into a sort of sub-Finbar Saunders) when we do chug off to Wheaton Aston (very early in the morning, I think); I visualise it as having turned into some kind of hellish blancmange (albeit not, hopefully, in the shape of a giant rabbit) that will have to be sliced up with cheesewire and stirred with a stick before struggling down the pumpout hose like an antelope being consumed by a boa constrictor.

Still, fortunately for me, when he was a boy Jim always wanted to be the man that drove the tanker and went round emptying people's septic tanks. Think how rarely people get to realise their childhood ambitions, even in a small way!