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2008 AMC 10A Problem 1

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2008 AMC 10A Problem 1AMC 10 Step by Step
Name:                             Date: October 28, 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 as long: 8 hours after the 8:30 AM start.

Solution

1. First find how long the machine has been running. From 8:30 AM to 11:10 AM is 22 hours 4040 minutes.
2. In that time it did one third of the job. The machine runs at a steady speed, so the whole job takes three times as long:
3×(2 h 40 min)=6 h 120 min.3 \times (2\text{ h } 40\text{ min}) = 6\text{ h } 120\text{ min}.
3. Since 120120 minutes is 22 hours, the whole job takes 88 hours.
4. The whole job started at 8:30 AM, so count the 88 hours from there: 8:30 AM plus 88 hours is 4:30 PM.

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

Why this works

When a machine works at a steady speed, time and work grow together: one third of the work takes one third of the time. The only care needed is to add the total time to the moment the job started, not to the moment you were told about.

Alternative approach

Count only what is left. Two thirds of the job remain, which takes twice as long as the first third: 2×(2 h 40 min)=5 h 20 min2 \times (2\text{ h } 40\text{ min}) = 5\text{ h } 20\text{ min}. Starting from 11:10 AM, add 55 hours to get 4:10 PM, then 2020 more minutes to get 4:30 PM.

The trap

Adding 8 hours to 11:10 AM instead of to the 8:30 AM start, or adding only the leftover time to the start.

Concise 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}}.

Review in the AoPS books

Techniques

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