To find when Nicole and Elizabeth will be on the same page of the book, we will first express their pages in terms of \( t \), the number of days into the month.
For Nicole, who starts on page 36 and reads 2 pages per day: \[ N(t) = 36 + 2t \]
For Elizabeth, who starts on page 4 and reads 10 pages per day: \[ E(t) = 4 + 10t \]
We want to find the value of \( t \) when Nicole and Elizabeth are on the same page, which means we set \( N(t) \) equal to \( E(t) \): \[ 36 + 2t = 4 + 10t \]
Now we solve for \( t \). First, rearranging the equation gives: \[ 36 - 4 = 10t - 2t \] \[ 32 = 8t \] \[ t = \frac{32}{8} = 4 \]
Conclusion:
After 4 days, \( t = 4 \), Nicole and Elizabeth will be on the same page of the book.
Checking:
Now we can check the pages they will be on after 4 days:
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For Nicole: \[ N(4) = 36 + 2(4) = 36 + 8 = 44 \]
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For Elizabeth: \[ E(4) = 4 + 10(4) = 4 + 40 = 44 \]
Thus, both Nicole and Elizabeth will be on page 44 after 4 days.
Graphing:
To illustrate, you can plot the two functions \( N(t) \) and \( E(t) \) on a graph:
- The function \( N(t) = 36 + 2t \) is a straight line with a y-intercept at 36 and a slope of 2.
- The function \( E(t) = 4 + 10t \) is also a straight line with a y-intercept at 4 and a slope of 10.
At \( t = 4 \), the two lines intersect, confirming they are on the same page after 4 days.
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