Liverpool Open Maths Challenge '04

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Its that time of year again, wasnt sure whether to put this in maths or in challanges, never mind.

 

Have a go see what you think, mabye a new pair of jogging bottoms for the brain eh? Ill put my solution up in a week or so, with the answers.

 

1.A churchwarden lives lives on a farm which is 200 meters from the nearest point, Pm on a straight road. 800m from P along the road is a chruch. The church warden can walk at 6kmh-1 over his farm and at 10kmh-1 along the road. What distance from P must he aim to meet the road in order to reach the church as quickly as possible?

 

2.The verger has 9 pieces of chain; -0-, -0-0, -0-0-, -0-0-, -0-0-0, -0-0-0,

-0-0-0. -0-0-0-, -0-0-0-0-0. He wants to joint them into one endless chain of 50 links. It will cost 50p to open any link and £1 to weld together again, but he could buy a new chain of fity links of the same quality for £13, what should he do?

 

3.The churchwardens estate is made up of three square fields, containing 18, 20 and 26 acres. The fields touch corners in the middle leaving a triangle in the middle. In orger to put a ring fence around his fence he bought four triangular fields (between each two of the fields). what is the total area of the estate?

 

4. On 1 of the outings arranged byt the sunday club the childeren from only 4 families where able to attend. The vicar asked how many childeren would be going? all the families have a different number of childeren and there are fewer than 18. And the product of the childeren in each family is the total number of steps up the bell tower. Is there an only child? When he was told the answer he knew how many childeren there were. How many?