Maths Olympiad Prep

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, 2016

Algebra Difficulty 1.5 Junior Find the answer Canada

Hicham runs 16 km in 1.5 hours. He runs the first 10 km at an average speed of 12 km/h. What is his average speed for the last 6 km?

Pick one

Solution

When Hicham runs 10 km at an average speed of 12 km/h, he takes 1012=56\frac{10}{12} = \frac{5}{6} hours to run this distance.

Since Hicham runs for a total of 1.5 hours, then he runs the last 6 km in 3256=9656=46=23\frac{3}{2} - \frac{5}{6} = \frac{9}{6} - \frac{5}{6} = \frac{4}{6} = \frac{2}{3} hours.

Since he runs 6 km in 23\frac{2}{3} hours, his average speed for this segment is 62/3=9\frac{6}{2/3} = 9 km/h.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.