Traveller’s Arithmetic | | DJS

Traveller’s Arithmetic

1.  Fred is going to visit Ireland. He buys Travellers’ Cheques to the value of £300 at an exchange rate of 1.605 Euros to the pound and pays 1% commission on any conversion. So how many Euros will he have if he converts all of his Travellers’ Cheques to Euros?

2.  Last year, 2006, Fred went to South Africa. Having prepared himself with Travellers’ Cheques from Lloyds at no charge he was a little surprised to find the Bureau de Change at Cape Town International advertising “no commission on Travellers’ Cheques” but when he asked to exchange some Travellers’ Cheques to Rand he was told there would be a charge of 70 Rand. There are between 11 and 12 Rand per pound Sterling. 

a.    How big was the charge in Sterling? 

b.    How much money would he need to convert to make the 70 Rand charge better value than 1% commission? 

3.    Fred hired a car to help him explore the Cape peninsula. That cost him £460 when the conversion rate was R11.60 to the pound. He covered 4500 kilometres. Fuel cost typically 200 Rand for 700km driving.

a.    What was the hire charge in Rand?

b.    To the nearest hundred Rand, how much did he spend on fuel?

c.    If he spent that rounded amount on fuel, what was his cost in Rand per 100km?

d.    Show that 45 miles per gallon equates to 6.27 litres per 100km.

e.    Estimate how many times more expensive fuel was in Britain compared to South Africa, assuming Fred’s car managed to return 45 miles per gallon. nin 2006 petrol was 86 to 96p per litre. Look the current figures up for UK and RSA and repeat the calculation.

4.    On the way home from South Africa, the plane calls at Schiphol in Amsterdam. Fred will have to use some Euros to help while away the three or four hours of the stop over. If the total distance from Cape Town to London is something like 6900km and if the plane generally flies at 900 kmph, then

a.  Just how short could the flight have been? Add half an hour back on for acceleration and deceleration.

b.    The whole trip back took 23 hours from check-in to reaching home. What was the average speed?

c.    What was the effect on the average speed by adding each hour at Schiphol?

 1   £300x1.605=€481.5, less 1% => €476.68 rounded down because even if all done on a single conversion, it would be.2    ZAR 70, or R70 is £5.83 to £6.36     For this charge to be 1%, he exchanges £583 to £636 (you might multiply by 99 instead, £524.7 to £629.60) but since trvellers cheques come in round amounts such as £50, we’re looking at answers from £550 upwards: At £550 it is close and the exchange rate makes a difference; from £650 onwards the fixed charge is a smaller cost. Note that already the answer is not the black and white one so many students expect Maths to provide. Life is not like that.3     £460 converts to R 5336. Of course, he may have paid commission too.     4500 / 700 * R200 = R1285.71, so R1300. R1300 / 4500 x 100 = R28.89 per 100km     45mpg => 1/45 gal/mile = 1/45 x gal/mile x miles/100km x litres/gal = 1/45 x 100/1.609344 x 4.54/1 = 6.26895, so 6.27 litres per 100km. Look up fuel prices in RSA and UK for the month you do the question.
4     6900/900 => 7 hours 40 minutes minimum, probably over 8.
       6900 / 23 hours =>300 kph. 3 hours at Schiphol gives 6900/20, 345kph, 4 gives 363kph, 5 gives 383kp, and looking at the other side of 3 hours, two gives 6900/21, 329kph. 


Fred was me. For reasons I still can't explain sensibly, I went to Cape Town for a half-marathon, in I think 2006; to make the trip worthwhile I added ten days exploring and actually hired a guy to show me around. I drove, he 'fixed' things like where we stayed. Fantastic trip. Also went to see a guy from the first maths lesson taught by me. Poor guy is still damaged by the experience. As for the race, I only just finished in the top 4%, about standard for me then.

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