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MathNet 2021 — Part 08 Question 35

Math Olympiad Vault · MathNet 2021 — Part 08

Question 35

Ana and Meta left the village of Zabukovje for the village of Zahrastje at the same time, Ana by bicycle and Meta by car. Ana travelled at a constant speed of $30\,\mathrm{km/h}$ and Meta at a constant speed of $70\,\mathrm{km/h}$. After reaching Zahrastje, Meta stayed there for $1\,\mathrm h$ and then drove back towards Zabukovje at the same speed of $70\,\mathrm{km/h}$. On her return journey she met Ana $105\,\mathrm{km}$ from Zahrastje. How many kilometres apart are the two villages?
  1. 262.5
  2. 300
  3. 315
  4. 345
  5. 375