1) 20 mph

         2) 37, 51, 60, 65, 87

         3) (a) 9    (b) 265

    Notes

  1). Suppose normal speed = v mph
      Then normal time = 5/v hrs.

      So  5/(v + 10) = 5/v - 1/12

      Solving,  v = 20  (or v = -30   ! )

  2). By intelligent trial and error.

  3). The following is a general solution:
        Let f(n,m) represent the number of arrangements of
        the numbers 1 to n with exactly m in their correct
        positions. It is easy to show that
          f(n,m) = nCm f(n-m,0) (where nCm is the number of
        selections of n objects takem m at a time).

      This enables the following table to be built one
        column at a time, using also the fact that the total
        for each column must be factorial n.

            n  = 1    2    3    4    5    6    (etc)
       m =  0    0    1    2    9    44   265
            1    1    0    3    8    45   264
            2         1    0    6    20   135
            3              1    0    10    40
            4                   1     0    15
            5                         1     0
            6                               1

       Alternatively, solution by computer is possible.     

  1. Two oranges and three lemons cost 119 pence. If an
     orange costs 7p more than a lemon, what does a
     lemon cost? 

  2. Andrew and Barry together have £29 in their pockets,
     Barry and Charles together have £40, while Charles
     and David together have £65. David has twice as much
     as Andrew. How much has Barry? 

  3. A wine-glass contains 10 cl of wine, and a water-jug
     contains 100 cl of water. If 1 cl of water is taken
     from the jug and well mixed with the wine, and then
     1 cl of the mixture is returned to the water-jug, which
     is greater, the volume of water in the wine or wine in
     the water?