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Problem 156

Algebra Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2022

Mayar and Rosie are 90 metres apart. Starting at the same time,
they run towards each other. Mayar runs twice as fast as Rosie. How far
has Mayar run when they meet?

Pick one

Official solution

Suppose that Rosie runs $x$
metres from the time that they start running until the time that they
meet.

Since Mayar runs twice as fast as Rosie, then Mayar runs $2x$ metres in this time.

When Mayar and Rosie meet, they will have run a total of 90 m, since
between the two of them, they have covered the full 90 m.

Therefore, $2x + x = 90$ and so $3x = 90$ or $x
= 30$.

Since $2x = 60$ , this means that
Mayar has run 60 m when they meet.

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