AMC 10A/12A 2024 (Problem 2/2)

A model used to estimate the time it will take to hike to the top of the 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?

\text{(A)}\;240

\text{(B)}\;246

\text{(C)}\;252

\text{(D)}\;258

\text{(E)}\;264