2008 AMC 12A Problem 1

Attempt Problem 1 of the 2008 AMC 12A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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
Answer: D
Concepts:ratio and proportiondate and time
Small hint:
Find how long it took to finish the first third of the job
Big hint:
The whole job takes three times as long as that first third
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 3⋅160=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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