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.
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.