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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?
If we denote Alan by A, Brian by B, Charles by C and Dave by D we can find the answer in the following way. Since A + B + C = D and A + B + C + D = 44, it is easy to see that D has 22 sheep. So A + B + C = 22. We can use this along with the two other facts, A + 3 = B  1 and C  3 = 3A, to find that A has 3, B has 7, C has 12 and D has 22. In a little more detail:
A + B + C = 22 (1)
A + 3 = B  1 (2)
C  3 = 3A (3)
Rearrange (3) to give C = 3A + 3 and replace the C in (1) to give A + B + 3A + 3 = 22. Simplified this gives B = 19  4A (4). Rearrange (2) to give B  A = 4. Use (4) in the place of B to give 19  4A  A = 4 to give A = 3. Now use A to work out B, and then C.
Puzzle 51
Move from letter to letter and collect the necessary letters for FIND (in any order).
How many different routes can you take if you always start with the central F and always move either horizontally or vertically?
 the cold tap could fill 72 baths
 the hot tap could fill 48 baths
 the plug could drain 90 baths
 the leak could drain 12 baths
Therefore, in 24 hours, we have 72 + 48  90  12 baths full = 18 baths.
Therefore each bath would take 80 minutes to fill.
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