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Source: 2024 AIME I Problem 1

February 2, 2024
AMCAIMEAIME I

Problem Statement

Every morning, Aya does a 99 kilometer walk, and then finishes at the coffee shop. One day, she walks at ss kilometers per hour, and the walk takes 44 hours, including tt minutes at the coffee shop. Another morning, she walks at s+2s+2 kilometers per hour, and the walk takes 22 hours and 2424 minutes, including tt minutes at the coffee shop. This morning, if she walks at s+12s+\frac12 kilometers per hour, how many minutes will the walk take, including the tt minutes at the coffee shop?