2023 AMC 8 Problem 9

Below is the video solution and professionally curated solution for Problem 9 of the 2023 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.

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Concepts:data and graph interpretation

Difficulty rating: 1020

9.

Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between 44 and 77 meters?

66

88

1010

1212

1414

Video solution:
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Written solution:

The first time that she hits an elevation of 77 meters is at 22 seconds.

She then dips below 44 meters after 44 seconds. This adds 42=24 - 2 = 2 seconds to the total answer.

Malaika then goes above 44 meters at 66 seconds. She hits 77 meters again at 1010 seconds.

This adds 106=410 - 6 = 4 more seconds to the total. She finally dips below 77 meters for the last time at 1212 seconds.

She then falls below 44 meters at 1414 seconds, finally adding 1412=214 - 12 = 2 seconds to the total time.

The desired answer is therefore 2+4+2=8 seconds.  2 + 4 + 2 = 8 \text{ seconds. } Thus, B is the correct answer.

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