Question

the graph represents the heights of two climbers on a climbing wall over a 12-minute time period. which statement is true about the climbers heights? brynn was resting at a constant climbing height when abbys climbing height was decreasing. abbys climbing height was decreasing when brynns climbing height was increasing. the heights of both climbers increased, then decreased, with no rest at a constant height. both climbers rested on the wall at a constant height for 2 minutes.

Explanation:

Step1: Analyze each option

- Option 1: When Abby's height was decreasing (after minute 8), Brynn's height was also decreasing (from minute 10 to 12? No, Brynn's height started decreasing after minute 8? Wait, looking at the graph: Abby's climb (brown) has a flat part (rest) around minutes 4 - 6? Wait, no, the blue is Brynn, brown is Abby. Wait, Abby's graph (brown) goes up, then flat (rest), then up, then down. Brynn's (blue) goes up, flat, up, then down. Wait, when Abby's height is decreasing (after minute 8), Brynn's height: at minute 8 - 10, Brynn's height is decreasing? Wait, no, the blue line: from minute 0 - 4, up; 4 - 6, flat (rest); 6 - 7, up; 7 - 10, down. Abby's (brown): 0 - 4, up; 4 - 6, flat; 6 - 8, up; 8 - 12, down. So when Abby's height is decreasing (8 - 12), Brynn's height: 7 - 10, down; 10 - 12, Brynn is at 0? Wait, no, the blue line ends at minute 10 (height 0), brown at minute 12 (height 0). So when Abby's height is decreasing (8 - 12), Brynn's height: 8 - 10, decreasing (from 15 to 0? Wait, no, the blue line at minute 7 is at 15, then from 7 - 10, it goes down to 0. Abby at minute 8 is at 22, then down to 0 at 12. So when Abby's height is decreasing (8 - 12), Brynn's height is decreasing (7 - 10) and then at 0 (10 - 12). So Brynn was not resting (constant height) when Abby's was decreasing. So option 1 is false.
- Option 2: Abby's height decreasing: 8 - 12. Brynn's height increasing: when? Brynn's height increases 0 - 4, 6 - 7. So when Brynn's was increasing (6 - 7), Abby's height: at 6 - 7, Abby's height is increasing (from 15 to 22? Wait, Abby's graph at minute 6: let's see the grid. At minute 4, Abby is at 14; minute 6, 14 (flat); minute 8, 22. Wait, maybe my initial analysis was wrong. Let's re-examine the graph:

The x-axis is time (min), y-axis is height (feet).

Blue (Brynn):
- 0 - 4 min: height increases from 0 to 14 (so slope positive, increasing)
- 4 - 6 min: height constant (flat, rest) at 14
- 6 - 7 min: height increases from 14 to 15 (slope positive, increasing)
- 7 - 10 min: height decreases from 15 to 0 (slope negative, decreasing)
- 10 - 12 min: height 0 (flat, but already at bottom)

Brown (Abby):
- 0 - 4 min: height increases from 4 to 14 (slope positive, increasing)
- 4 - 6 min: height constant (flat, rest) at 14
- 6 - 8 min: height increases from 14 to 22 (slope positive, increasing)
- 8 - 12 min: height decreases from 22 to 0 (slope negative, decreasing)

Now, check option 2: "Abby’s climbing height was decreasing when Brynn’s climbing height was increasing." When is Brynn's height increasing? 0 - 4 min, 6 - 7 min.

During 0 - 4 min: Abby's height is increasing (0 - 4, Abby goes from 4 to 14, increasing). So no.

During 6 - 7 min: Abby's height: at 6 min, Abby is at 14 (flat from 4 - 6), then at 7 min, Abby's height: let's see, at 8 min, Abby is at 22. So from 6 - 8, Abby's height is increasing (from 14 to 22). So during 6 - 7 (Brynn increasing), Abby's height is increasing. So option 2 is false.

- Option 3: "The heights of both climbers increased, then decreased, with no rest at a constant height." Wait, both had flat parts (rest) at constant height: Brynn 4 - 6 min (height 14), Abby 4 - 6 min (height 14). So they did rest (constant height) for 2 minutes (4 - 6 min: 2 minutes). So option 3 says "no rest", which is false.

- Option 4: "Both climbers rested on the wall at a constant height for 2 minutes." Let's check the flat parts (constant height, rest):

Brynn: 4 - 6 min (from minute 4 to 6, that's 2 minutes) – height constant at 14.

Abby: 4 - 6 min (from minute 4 to 6, 2 minutes) – height constant at 14.

Yes! So both rested (constant height) for 2 minutes (4 - 6 min). So option 4 is true. Wait, but earlier I thought option 3 was false, which it is, because they did rest. So option 4 is correct.

Wait, but let's confirm the time for the flat part. From minute 4 to 6: that's 2 minutes (6 - 4 = 2). So both had a flat segment (constant height) from 4 to 6 minutes, which is 2 minutes. So option 4 is true.

Step2: Confirm the correct option

After analyzing each option, option 4 (Both climbers rested on the wall at a constant height for 2 minutes) is true.

Answer:

D. Both climbers rested on the wall at a constant height for 2 minutes (assuming the options are labeled A, B, C, D as per the order: first option A, second B, third C, fourth D)