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2017 AMC 10B Problem 2

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2017 AMC 10B Problem 2AMC 10 Step by Step
Name:                             Date: September 13, 2026
Linear Equations & Word Problems · difficulty 1 of 5 · about 2 min · position P1-10

Sofia ran 55 laps around the 400400 -meter track at her school. For each lap, she ran the first 100100 meters at an average speed of 44 meters per second and the remaining 300300 meters at an average speed of 55 meters per second. How much time did Sofia take running the 55 laps?

  1. A)

    5 minutes and 35 seconds\text{5 minutes and 35 seconds}

  2. B)

    6 minutes and 40 seconds\text{6 minutes and 40 seconds}

  3. C)

    7 minutes and 5 seconds\text{7 minutes and 5 seconds}

  4. D)

    7 minutes and 25 seconds\text{7 minutes and 25 seconds}

  5. E)

    8 minutes and 10 seconds\text{8 minutes and 10 seconds}

Answer

C

Key insight

Time equals distance over speed for each segment: 100/4 = 25 s plus 300/5 = 60 s gives 85 s per lap, times 5 laps.

Solution

Compute the time for one lap segment by segment.

  • First 100100 meters at 44 m/s: 1004=25\frac{100}{4} = 25 seconds.
  • Remaining 300300 meters at 55 m/s: 3005=60\frac{300}{5} = 60 seconds.

One lap takes 25+60=8525 + 60 = 85 seconds, so five laps take 5⋅85=4255 \cdot 85 = 425 seconds. Since 425=7⋅60+5425 = 7 \cdot 60 + 5, that is 77 minutes and 55 seconds.

The answer is (C) 7 minutes and 5 seconds\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}.

Why this works

Speeds do not add or average directly; times do. Whenever a trip has pieces at different speeds, compute each piece's time with t=d/vt = d/v and add. The final unit conversion (425425 s to min:sec) is where careless errors happen, so do it last and check it.

The trap

Averaging the two speeds to 4.5 m/s and dividing 2000 m by it, which ignores that the segments have different lengths.

Common mistakes

  • Averaging the two speeds to 4.5 m/s and dividing 2000 m by it, which ignores that the segments have different lengths.
  • Computing 8585 seconds per lap correctly but forgetting to multiply by 55, or misconverting 425425 seconds.

Techniques

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