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## Quiz of the Month (January 2004)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```    1.  2.5 denarii
2.  34
3.  40```

Notes
```  1. 7g + 5w = 37
5g + 7w = 35
Solving:    g = 3.5, w = 2.5

2. T + D + H + F = 37 X 4 = 148
T + D + H     = 40 X 3 = 120.  So F = 148-120 = 28
D + H + F = 32 X 3 =  96.  So T = 148-96  = 52
So  D + H     = 148-28-52 = 68

3. Suppose n = no. of visible steps,
v = escalator speed in steps/sec.
So time for a given step to travel from bottom to
top = n/v sec.
When Wally's speed = v + 1, time = n/(v + 1)
When Wally's speed = v + 2, time = n/(v + 2)
So n/(v + 1) = n/v - 36
n/(v + 2) = n/v - 45
Solving, n = 40, v = 2/3```

#### THIS MONTH'S QUIZ

As seen from the earth, the sun and moon appear as discs of identical diameters. Relative to the sun, the moon's disc appears to move through a distance equal to its own diameter in one hour. During a certain partial eclipse of the sun, at the moment of maximum eclipse (position B) the centre of the sun (point P) appears to coincide with a point on the moon's circumference.

 1. At the moment of maximum eclipse (position B) what proportion of the circumference of the sun's disc is visible? 2. At the moment of maximum eclipse what proportion of the area of the sun's disc is visible? 3. How long does the eclipse last, from the moment of first contact (position A) to the last contact (position C)?

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(c) Hector C. Parr (2004)

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