CEMC Fermat, 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 $\frac{10}{12} = \frac{5}{6}$ hours to run this distance.

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

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

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