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AIME 2024 / AIME 2024 train ec06db71-bc34-527f-87ca-fb9b7bbdd631

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Every morning Aya goes for a

9

-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of

s

kilometers per hour, the walk takes her 4 hours, including

t

minutes spent in the coffee shop. When she walks

s+2

kilometers per hour, the walk takes her 2 hours and 24 minutes, including

t

minutes spent in the coffee shop. Suppose Aya walks at

s+ rac{1}{2}

kilometers per hour. Find the number of minutes the walk takes her, including the

t

minutes spent in the coffee shop.

Plain-text mathematical notation (without MathML)

Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+rac12 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop.

Original LaTeX notation

Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, including $t$ minutes spent in the coffee shop. Suppose Aya walks at $s+rac{1}{2}$ kilometers per hour. Find the number of minutes the walk takes her, including the $t$ minutes spent in the coffee shop.

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Source and history

task_id: ec06db71-bc34-527f-87ca-fb9b7bbdd631
task_key: default--train--ec06db71-bc34-527f-87ca-fb9b7bbdd631
task_revision_id: 2
config / split: default / train

Official source

initial import