The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
We assume the minutes taken by Millie to catch up with Ben to be x minutes.
The number of words Ben has already typed = 180.
The unit rate for Ben for the typing of words = 30 per minute.
Therefore, words typed by Ben in x minutes = 30x words.
Therefore, the total number of words typed by Ben = 180 + 30x words.
The number of words Millie has already typed = 60.
The unit rate for Millie for the typing of words = 50 per minute.
Therefore, words typed by Millie in x minutes = 50x words.
Therefore, the total number of words typed by Millie = 60 + 50x words.
As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.
To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:
60 + 50x = 180 + 30x,
or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},
or, 60 + 20x = 180 {Simplifying},
or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},
or, 20x = 120 {Simplifying},
or, 20x/20 = 120/20 {Dividing both sides by 20},
or, x = 6 {Simplifying}.
Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.
Learn more about forming linear equations in one variable at
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