Medium Puzzles 

Workings

Hint
In order for the clocks to show the same time (e.g. 2 o'clock), what must the total time gained by one, and lost by the other, total?

Answers
Midnight, 10 days later, when they will both show 4 o'clock.
Midnight, 30 days later, when they will both show 12 o'clock.
Reasoning #1
In order for the clocks to show the same time, the total time gained by one, and lost by the other, must be 12 hours.

For example, if the first clock were to show 2 o'clock, it would have gained 2 hours. In order for the second clock to also show 2 o'clock, it would have had to have lost 10 hours. This is a total of 12 hours gained and lost.

We know that for every hour that passes, the first clock gains one minute, and the second clock loses 2 minutes, for a total time gained and lost of 1 + 2 = 3 minutes.

The total time gained and lost will equal 12 hours when 12 x 60 ÷ 3 = 240 hours have passed. 240 hours = 10 days.

The first clock will have gained 240 x 1 minutes = 240 minutes = 4 hours.

The second clock will have lost 240 x 2 minutes = 480 minutes = 8 hours.

So, they will both show 4 o'clock, 10 days later.

Reasoning #2
In the first answer, we can see that 10 days later, the clocks both show 4 o'clock.

If we move forward another 10 days, both clocks would show 8 o'clock.

If we move forward another 10 days, both clocks would show 12 o'clock.

This will now be the correct time.

So, they will both show 12 o'clock, 30 days later.

Workings

Hint
Another example, PEN is a complete word because:
   -en = ten
   p-n = pin
   pe- = pea

Answer
Two of the words are not complete: bugs, lean.

Reasoning
The remaining 8 words can be changed as follows:
hard:  -ard = card
 h-rd = herd
 ha-d = hand
 har- = harp

port:  -ort = fort
 p-rt = part
 po-t = poet
 por- = pore

duck:  -uck = muck
 d-ck = deck
 du-k = dusk
 duc- = duct

bugs:  -ugs = hugs
 b-gs = bags
 bu-s = buys
 bug- = ----

bail:  -ail = hail
 b-il = boil
 ba-l = bawl
 bai- = bait

mast:  -ast = cast
 m-st = most
 ma-t = malt
 mas- = mask

thin:  -hin = shin
 t-in = twin
 th-n = than
 thi- = this

lean:  -ean = mean
 l-an = loan
 le-n = ----
 lea- = leaf

fire:  -ire = hire
 f-re = fare
 fi-e = five
 fir- = firm

read:  -ead = bead
 r-ad = road
 re-d = reed
 rea- = real

Workings

Hint
This is a very common sequence.

Answer
X.

The last letters of the words one, two, three, four, five, six.

Workings

Hint
Try rewriting the clues so that those who finished ahead are written first.

Answer
Pat Piper                 (P)
 Alex Ardle               (A)
  Zeb Zebra               (Z)
   Frankie Flint          (F)
    Max Merrymood         (M)
     Jesse Jackson        (J)
      Glenn Goodfellow    (G)
       Toby Trent         (T)
        Billie Brick      (B)
         Kelly Kingfisher (K)

Reasoning
If we number the clues, write each name using a single letter, and rewrite the clues so that those who finished ahead are written first:

M beat T and J P beat J, T, and A P beat Z G beat T Z beat F F and P beat G T beat B A beat Z, K, and G G and M beat K B beat K A and Z beat M F beat T, M, and B J and A beat T J beat G and B
By (2): P A
By (8): P A Z
By (5): P A Z F
By (12): P A Z F M
By (1): P A Z F M J
By (14): P A Z F M J G
By (4): P A Z F M J G T
By (7): P A Z F M J G T B
By (10): P A Z F M J G T B K