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Hint: How many miles were left at the start of yesterday?
Answer: 336 miles.
On the first day I travelled one quarter of the distance (84, leaving 252). On day two, I travelled one half of the remaining distance (126, leaving 126). On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5). Yesterday I travelled one third of the remaining distance (10.5). I now have 21 miles left to travel.
To work these numbers out, it is easiest to start at the end and work backwards.
Yesterday I travelled 1÷3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 x 3÷2) at the start of yesterday.
On day 3 I travelled 3÷4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 x 4) at the start of day 3.
On day 2 I travelled 1÷2 of the distance to leave 126 miles, therefore there were 252 miles (=126 x 2) at the start of day 2.
On the first day I travelled 1÷4 of the distance to leave 252 miles, therefore there were 336 miles (=252 x 4÷3) at the start of the first day.
Puzzle 7
Last week I travelled from London to Leeds, which is a distance of 174 miles.
I started at 9.15am and completed the journey with an average speed of 40 miles per hour.
On the way back, in the evening, I travelled exactly the same route, starting at 5.15pm. The traffic was light and I completed the journey with an average speed of 60 miles per hour.
What was the overall average speed for round trip?
Hint: Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time.
Answer: 48 miles per hour.
Time = Distance ÷ Speed
Speed = Distance ÷ Time
The outward journey took 174 miles ÷ 40 mph = 4.35 hours.
The return journey took 174 miles ÷ 60 mph = 2.9 hours.
So I travelled a total of 2 x 174 = 348 miles. I did this in a total of 4.35 + 2.9 = 7.25 hours.
My overall average speed was therefore 348 miles ÷ 7.25 hours = 48 miles per hour.
Puzzle 8
Can you find a five digit number which has no zeros no digit is repeated, where:
The first digit is a prime number.
The second digit is the fifth digit minus the first digit.
The third digit is twice the first digit.
The fourth digit is the third digit plus three.
The fifth digit is the difference between the first digit and the fourth digit.
Don't forget that 1 isn't prime, so 13,254 isn't allowed.
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