# Puzzle ZOFE

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Yesterday I went for a short bicycle ride around the local lakes. As the weather was very hot, I rode in various stages.

In the first stage I rode half of the overall distance.

Stage two saw half of the remaining distance plus 35 metres covered.

Stage three covered three-quarters of the remaining distance.

Stage four completed half of the remaining distance plus 75 metres.

Stage five completed the journey with a final burst of 150 metres.

How far did I cycle in total?

7,340 metres.

Reasoning
Stage 5's clue tells us that there were 150m 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

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