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## Quiz of the Month (April 2003)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```  1.   32 mph
2.  22.5 mph or 50 mph
3.  01:36 pm.

Notes
1. The position of the hiker divides the length of the tunnel
internally in the ratio 3:5. So the position of the train
divides the length of the tunnel externally in the ratio 3:5.
So the train is 1.5 tunnel lengths from the tunnel entrance
(and 2.5 lengths from the exit). So train travels 1.5 lengths
while hiker travels 3/8 lengths, etc.

2. Total length of two trains = 210 + 120 = 330 m
So total time to pass each other = 330/(60 + v)
In this time A moves either 180 or 240 m.
So 60 X 330/(60 + v) = 180 or 240
Solving, v = 22.5 or 50.```

``` 3. Impose a Southerly velocity of 2.25 mph on the whole system.
Then Andy is reduced to rest, and Betty's velocity becomes as
shown. Note that 2.25:3 = 3:4, so the triangle of velocities
is a 3:4:5 triangle, and Betty's velocity is 3.75. Closest
approach is at X, and triangle SMX also is 3:4:5. So
MX = 6 ml. and time = 6/3.75 = 1.6 hr.```

#### THIS MONTH'S QUIZ

1. You are given a square of cardboard with sides of length 10 cm, and you are to cut off each of the four corners to produce a regular octagon. What is its area?

2. The top of a rectangular box has area 76 square cm, the front has area 57 square cm, and the side has area 48 square cm. Find the dimensions of the box.

3. Two vertical flag poles with heights of 13 m and 7 m respectively stand on level ground. A straight cord joins the top of each pole to the base of the other. How far above the ground is the intersection of the two cords?

***

(c) Hector C. Parr (2003)

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