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2015 AMC 10B Problem 2

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2015 AMC 10B Problem 2AMC 10 Step by Step
Name:                             Date: September 13, 2026
Clocks, Calendars & Time · difficulty 1 of 5 · about 1 min · position P1-10

Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task?

  1. A)

    3:10 PM\text{3:10 PM}

  2. B)

    3:30 PM\text{3:30 PM}

  3. C)

    4:00 PM\text{4:00 PM}

  4. D)

    4:10 PM\text{4:10 PM}

  5. E)

    4:30 PM\text{4:30 PM}

Answer

B

Key insight

From 1:00 to 2:40 is 100 minutes for two tasks, so each task is 50 minutes and the third ends 50 minutes after 2:40.

Solution

From 1:00 PM to 2:40 PM is 11 hour 4040 minutes, which is 100100 minutes. During that time Marie completed exactly two tasks (the first and the second), so each task takes
1002=50 minutes.\frac{100}{2} = 50 \text{ minutes}.

The third task starts at 2:40 PM and lasts 5050 minutes: 2020 minutes bring her to 3:00 PM, and the remaining 3030 minutes bring her to 3:30 PM.

The answer is (B) 3:30 PM\boxed{\textbf{(B)}\ \text{3:30 PM}}.

Why this works

Convert clock times to minutes before dividing; a "1:40" gap is 100100 minutes, not 140140. The only other thing to get right is how many tasks fit in the measured interval: the finish of the second task marks two tasks, not three.

The trap

Reading 1:00 to 2:40 as 1.4 hours = 140 minutes (decimal time), or dividing the elapsed time by three tasks instead of two.

Common mistakes

  • Reading 1:00 to 2:40 as 1.4 hours = 140 minutes (decimal time), or dividing the elapsed time by three tasks instead of two.
  • Adding the 5050 minutes to 2:40 carelessly (writing 2:90 and misconverting it), or adding only 3030 minutes and landing on 3:10, choice (A).

Techniques

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