Puzzle 5
How much soil is there …
… in a circular hole 2 metres deep and 1 metre across?
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Hint
How much soil is in any hole?
Puzzle 7
I travelled from London to Glasgow last week at 60 miles per hour, I had filled my petrol tank just before I left, so it was full with 25 gallons.
Unfortunately, my petrol tank sprang a leak immediately, and I only managed to drive 300 miles before I ran out of petrol.
My car does 30 miles per gallon, how fast was I losing petrol through the hole?
Puzzle Copyright © Kevin Stone
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Hint
How much petrol was used for the journey itself?
Answer
3 gallons each hour.
Reasoning
I drove 300 miles at 30 miles per gallon, so I used 10 gallons. Which means I lost the other 15 gallons.
I drove the 300 miles at 60mph, which took me 5 hours.
So I lost 15 gallons of petrol in 5 hours = 3 gallons per hour.
Puzzle 8
In my money box, I found $36.80 made up of equal numbers of quarters, dimes, and nickels.
How many of each coin did I find?
Puzzle Copyright © Kevin Stone
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Hint
Remember that a quarter is 25c, a dime is 10c and a nickel is 5c.
Answer
92 of each coin.
Reasoning
There are an equal number of quarters, dimes and nickels, so we know that the answer must be a multiple of:
25c + 10c + 5c = 40c
and:
3680c ÷ 40c = 92 coins.
