Yesterday I went for a short bicycle ride around the local lakes. As the weather was very hot, I rode in shorter stages than I'd normally ride.
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?
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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
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