2008 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2008 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12A solutions, or check the answer key.

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Concepts:ratio and proportiondate and time

Difficulty rating: 800

1.

A bakery owner turns on his doughnut machine at 8 ⁣: ⁣308\!:\!30 am. At 11 ⁣: ⁣1011\!:\!10 am the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?

1 ⁣: ⁣501\!:\!50 pm

3 ⁣: ⁣003\!:\!00 pm

3 ⁣: ⁣303\!:\!30 pm

4 ⁣: ⁣304\!:\!30 pm

5 ⁣: ⁣505\!:\!50 pm

Solution:

From 8 ⁣: ⁣308\!:\!30 am to 11 ⁣: ⁣1011\!:\!10 am is 22 hours 4040 minutes, or 160160 minutes, to complete one third of the job.

The whole job then takes 3160=4803 \cdot 160 = 480 minutes, or 88 hours. Adding 88 hours to 8 ⁣: ⁣308\!:\!30 am gives 4 ⁣: ⁣304\!:\!30 pm.

Thus, D is the correct answer.

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