Random Puzzles 

Workings

Hint
Sometimes the easiest explanations are the best.

Answer
The other end of the rope is not tied to anything!

Workings

Hint
Try working backwards.

Answer
120 miles.

Reasoning
I now have 5 miles left to travel, so I must have travelled 5 miles yesterday.

At the end of Day 3, I had 10 miles left to travel, so I must have had 40 miles left at the start of the Day 3.

At the end of Day 2, I had 40 miles left to travel, so I must have had 60 miles left at the start of the Day 2.

At the end of Day 1, I had 60 miles left to travel, so I must have had 120 miles left at the start of the Day 1.

Double-Checking
On the Day 1, I travelled 60 miles, leaving 60 miles.

On Day 2, I travelled 20 miles, leaving 40 miles.

On Day 3, I travelled 30 miles, leaving 10 miles.

Yesterday, I travelled 5 miles, leaving 5 miles.

Workings

Hint
The word begins with the letter T.

Answer
Tattooists.

Which has 10 letters.

Workings

Hint
Try working backwards.

Answer
7,340 metres.

Reasoning
Stage 5's clue tells us that 150m was left. So the distance left at the start of Stage 4 must have been:
Dist4 = Dist4 + 75 + 150
        —————
          2

Which simplifies to give Dist4 = 450m.

Stage 3's clue tells us that 450m was one quarter of the remaining distance, so Dist3 = 1,800m.

Stage 2's clue tells us that the distance at the start of Stage 2 was:
Dist2 = Dist2 + 35 + 1800
        —————
          2

Which simplifies to give Dist2 = 3,670m.

Stage 1's clue tells us that 3,670m was half the overall distance, which means the entire ride was 7,340m.

Double-Checking
Starting with 7,340m:
Stage 1: cycled 3,670m, leaving 3,670m

Stage 2: cycled 1,870m, leaving 1,800m

Stage 3: cycled 1,350m, leaving   450m

Stage 4: cycled   300m, leaving   150m

Stage 5: cycled   150m, leaving     0m