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Workings

Hint
helium = h-- + l--

Answers
helium = hum + lie latest = let + sat almond = man + old eldest = led + set placed = cap + led radium = air + mud desert = red + set wealth = law + the tricky = cry + kit funnel = elf + nun
Alternative Answers
The following answers use less common words.

helium = him + leu
helium = hue + mil
helium = hum + lei

latest = els + tat

almond = don + lam
almond = lam + nod

eldest = eld + set
eldest = els + ted

placed = pec + lad

radium = mud + ria
radium = amu + rid
radium = aid + rum

wealth = awl + the
wealth = haw + let

There are more answers with even rarer words, but I've chosen not to include those.

Workings

Hint
This is a very common sequence.

Answer
A.

August, from initial letters of the months of the year.

Workings

Hint
The first letters of the words are: R, C, G, C, L, H, E, B, L.

Answers
18 8 9 14 15          = rhino 3 18 15 3 15 4 9 12 5 = crocodile 7 9 18 1 6 6 5        = giraffe 3 8 5 5 20 1 8        = cheetah 12 5 15 16 1 18 4     = leopard 8 9 16 16 15          = hippo 5 12 5 16 8 1 14 20   = elephant 2 21 6 6 1 12 15      = buffalo 12 9 15 14            = lion

Workings

Hint
How many miles were left at the start of yesterday?

Answer
336 miles.

Reasoning
To work these numbers out, it is perhaps easier 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 ÷ ²/₃) 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 ÷ ¹/₄) 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 ÷ ¹/₂) at the start of day 2.

On day 1, I travelled ¹/₄ of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ ³/₄) at the start of day 1.

Double-Checking
On day one, 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.