oldSTAGER No.90
February/March 2005

 

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"Christmas" Quiz

My driver and his car are too reliable and consistent. Whenever I accompany them on a HRCR road rally our regularity times are always predictable. Whatever the conditions we always average the same speed according to the class of road used. Of course, unless the distance and type of roads on an event match the usual performance of driver and car, we will never be in contention to win an event.
On the recent overnight Tour of Essexshire Rally there were three regularities with a single time control at the end of each one. The table below shows the mileage on classified (A and B) roads, yellow roads and white roads, and the time we took in minutes. 
 
Regularity Classified
Roads
Yellow
Roads
White
Roads
Time
Taken
1 6 15 8 75
2 10 6 12 59
3 12 9 4 56

We were penalised one minute for every minute late or early and overall our time penalties were 20 minutes. Needless to say we never made the top ten placings. 

1) What was our average speed on each type of road?

After the event at breakfast, while my predictable driver was tucking into his predictable greasy breakfast he happened to ask what the required average speeds were on each regularity. When I replied, his eyes glazed over momentarily before he asked (with baked bean juice running down his chin and chewed mushrooms splattering my Basic Roamer):
"Did you know those speeds and distances before we left the start?"
"Yes," I replied, "I had the route one hour before we left."
There was more glazing and bean juice.
"You stupid black bird, we could have cleaned those regularities."
"Er, how so, oh predictable one?" I snided.
He went on to explain that he had a secret shopping list of modifications which could adjust our standard average speed up or down by class of road. These were the possibilities:

  Modification Effect on Average Speed
a) England flag attached to aerial -2 mph on all roads
b) Speed camera detector on dashboard +1 mph on all roads
c) No Basic Roamer for navigator -3 mph on all roads
d) Average speed tables in nautical miles -8 mph on classified roads
e) Boot load of Christmas presents -11 mph on classified roads
f) Greasy breakfast dispenser for driver +1 mph on classified roads
g) Furry reindeer hanging from interior mirror +7 mph on yellow roads
h) Photo of Colin McRae in the glove box +4 mph on yellow roads
i) Santa suit for navigator + 6mph on yellow roads
j) Alcoholic Christmas pudding in the fuel tank +9 mph on white roads
k) Lead weights in driving shoes +3 mph on white roads
l) Handbrake decorated in tinsel +2 mph on white roads

2) Given that the required average speeds were 29, 28 and 25 mph, which modifications (by letter) should we have used to clean the event?


Solution from oldSTAGER 91

For part 1), if x was the speed in mph on classified roads, y on yellow roads and z on white roads, you had to solve the simultaneous equations for each regularity:
6/x + 15/y + 8/z = 75/60, 10/x + 6/y + 12/z = 59/60 and 12/x + 9/y + 4/z = 56/60
This gave x = 40, y = 18, z = 30.
For part 2) the overall average speeds required were given, and since the speeds numerically matched the mileage of each regularity, the ideal time to complete each one was one hour. Hence, the new equations to solve were:
6/x + 15/y + 8/z = 1, 10/x + 6/y + 12/z = 1 and 12/x + 9/y + 4/z = 1
This gave x = 20, y = 30 and z =40. The modifications to adjust to the required speeds were: a), b), d), e), g), i), j), and l).