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2008 AMC 10A Problem 1

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2008 AMC 10A Problem 1AMC 10 Step by Step
Name:                             Date: September 13, 2026
Clocks, Calendars & Time · difficulty 1 of 5 · about 1 min · position P1-10

A bakery owner turns on his doughnut machine at 8:30 AM\text{8:30}\ {\small\text{AM}} . At 11:10 AM\text{11:10}\ {\small\text{AM}} the machine has completed one third of the day's job. At what time will the doughnut machine complete the job?

  1. A)

    1:50PM\text{1:50} {\small\text{PM}}

  2. B)

    3:00PM\text{3:00} {\small\text{PM}}

  3. C)

    3:30PM\text{3:30} {\small\text{PM}}

  4. D)

    4:30PM\text{4:30} {\small\text{PM}}

  5. E)

    5:50PM\text{5:50} {\small\text{PM}}

Answer

D

Key insight

One third of the job took 2 hours 40 minutes, so the whole job takes three times that, 8 hours, starting from 8:30 AM.

Solution

From 8:308{:}30 AM to 11:1011{:}10 AM is 22 hours 4040 minutes, and in that time one third of the job was done.

The machine works at a constant rate, so the full job takes three times as long:
3×(2 h 40 min)=6 h 120 min=8 hours.3 \times (2\text{ h } 40\text{ min}) = 6\text{ h } 120\text{ min} = 8\text{ hours}.

Eight hours after the 8:308{:}30 AM start is 4:304{:}30 PM.

The answer is (D) 4:30 PM\boxed{\textbf{(D)}\ \text{4:30 PM}}.

Why this works

A constant-rate job is proportional: the time for the whole is the time for the fraction divided by that fraction. Convert the clock interval to minutes (or hours and minutes) before scaling, then add the total duration to the start time.

Alternative approach

Two thirds of the job remain and will take 2×2 h 40 min=5 h 20 min2 \times 2\text{ h }40\text{ min} = 5\text{ h }20\text{ min}. Adding that to 11:1011{:}10 AM gives 4:304{:}30 PM.

The trap

Adding the 8 hours to 11:10 AM (the one-third mark) instead of to the 8:30 AM start, or adding only the remaining 5 h 20 min to 8:30.

Common mistakes

  • Adding the 8 hours to 11:10 AM (the one-third mark) instead of to the 8:30 AM start, or adding only the remaining 5 h 20 min to 8:30.
  • Treating 22 h 4040 min as 2.42.4 hours when converting, which throws the total off.

Techniques

Set up the equation/formula and compute; no special trick needed