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MathNet 2024-part-05 — 168 problems (EN–VI) Question 121

Math Olympiad Vault · MathNet 2024-part-05 — 168 problems (EN–VI)

Question 121

A model used to estimate the time it will take to hike to the top of a mountain on a trail is of the form $T = aL + bG$, where $a$ and $b$ are constants, $T$ is the time in minutes, $L$ is the length of the trail in miles, and $G$ is the altitude gain in feet. The model estimates that it will take 69 minutes to hike to the top if a trail is 1.5 miles long and ascends 800 feet, as well as if a trail is 1.2 miles long and ascends 1100 feet. How many minutes does the model estimate it will take to hike to the top if the trail is 4.2 miles long and ascends 4000 feet?
(A) 240 (B) 246 (C) 252 (D) 258 (E) 264