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MathNet 2022-part-03 — 197 problems (EN–VI) Question 47

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 47

Viale Marconi is $800~\mathrm{m}$ long; $200~\mathrm{m}$ from one end there is a parking meter, and $100~\mathrm{m}$ from the opposite end there is a clothes shop. Astolfo wants to park his car, get a ticket at the parking meter, go back to the car to display it on the windscreen, visit the shop and finally return to the car. Moreover, he is lazy and so he wants to walk as little as possible; where should he park to do so? Indicate the set of points of the street that minimise the distance Astolfo has to walk.
(A) The point in front of the parking meter
(B) The point in front of the shop
(C) The midpoint between the parking meter and the shop
(D) All points of the street
(E) All points of the stretch of street between the parking meter and the shop.