Questions: Meredith is addressing envelopes for a charity event. She has finished addressing 30 envelopes and is addressing more envelopes at the rate of 6 envelopes per hour. y=6x+30 Meredith's sister, Lily, joined her immediately and started addressing at the rate of 9 envelopes per hour, y=9x The number of envelopes addressed by both are shown in the graph. After how many hours will the number of envelopes addressed by Meredith and Lily be the same?

Meredith is addressing envelopes for a charity event. She has finished addressing 30 envelopes and is addressing more envelopes at the rate of 6 envelopes per hour. y=6x+30 Meredith's sister, Lily, joined her immediately and started addressing at the rate of 9 envelopes per hour, y=9x The number of envelopes addressed by both are shown in the graph. After how many hours will the number of envelopes addressed by Meredith and Lily be the same?
Transcript text: Meredith is addressing envelopes for a charity event. She has finished addressing 30 envelopes and is addressing more envelopes at the rate of 6 envelopes per hour. \[ y=6 x+30 \] Meredith's sister, Lily, joined her immediately and started addressing at the rate of 9 envelopes per hour, \[ y=9 x \] The number of envelopes addressed by both are shown in the graph. After how many hours will the number of envelopes addressed by Meredith and Lily be the same?
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Solution

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Solution Steps

Step 1: Find the intersection point of the two lines

The graph shows the number of envelopes addressed by Meredith and Lily. The x-axis represents the number of hours, and the y-axis represents the number of envelopes. The intersection point of the two lines represents the time when Meredith and Lily have addressed the same number of envelopes. The intersection point is at x = 10, y = 90.

Step 2: Determine the number of hours

The x-coordinate of the intersection point represents the number of hours when Meredith and Lily have addressed the same number of envelopes. In this case, x = 10.

Final Answer

\\(\boxed{10 \text{ hours}}\\)

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