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Quiz of the Month (December 2002)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

   1.  2 hrs.   
   2.  105
   3.  65


Notes

1. In one minute, gravel added = 1/60 + 1/40 - 1/30 = 1/120 truckful. So number of minutes required = 120.
2. If rows contain alternately 10 and 9 circles, the lines of centres are separated by 0.866 cm (applying Pythagoras to triangle AMC). So eleven rows occupy 0.5 + (10 X 0.866) + 0.5 = 9.66 cm.
Then no. of circles = 10+9+10+9+10+9+10+9+10+9+10 = 105.
3. The maximum number of squares is achieved by arranging them symmetrically in rows. Nine rows are possible, with nine squares in the middle row. The number of squares in the other rows can be checked with Pythagoras, and the total is 4+7+8+9+9+9+8+7+4 = 65.

THIS MONTH'S QUIZ

1. I used to fill up my tank with 25 litres of petrol. But now that the price has increased by 7p per litre I shall buy only 23 litres, to keep the cost the same as before. What does a litre of petrol cost now?

2. The 08:00 express from Kings Cross to York arrives at 10:00, while the 08:30 from York to Kings Cross arrives at 10:30. Assuming both trains travel at constant speed, at what time should they pass each other?

3. On one occasion the train from Kings Cross departed and arrived on time, but the train from York departed 30 minutes late and arrived 60 minutes late. Again assuming constant speeds, at what time did they pass each other?


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(c) Hector C. Parr (2002)


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