**Answer:** 7,340 metres.

---- Solution ----

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

---- Solution Method ----

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

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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

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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.