Two cyclists, A and B

MATHEMATICS · Multi-part · CBSE · Mathematics · Proportional Reasoning · Proportional Reasoning

Problem

Two cyclists, A and B, travel the same straight 40 km40\,\text{km} route but use different patterns of speed. Cyclist A: • First 10 km10\,\text{km} at 15 km/h15\,\text{km/h}, • Next 20 km20\,\text{km} at 5 m/s5\,\text{m/s}, • Last 10 km10\,\text{km} at 12 m/s12\,\text{m/s}. Cyclist B: • First 20 km20\,\text{km} at 600 m/min600\,\text{m/min}, • Remaining distance at 18 km/h18\,\text{km/h}. Answer the following. (a) Convert every speed used by cyclist A into m/s\text{m/s}. (b) Convert both speeds used by cyclist B into m/s\text{m/s}. (c) Calculate the total time taken by each cyclist to complete the route. (d) Who completes the route first and by how many minutes? (e) Briefly comment on how a slower segment can affect the overall average speed of a journey.

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