To find the unit rate, we divide the amount of lawn mowed (23) by the time it took to mow that amount of lawn (12 hours).
Unit rate = 23/12
Simplifying this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 1.
Unit rate = 23/12 = 1 11/12
Therefore, Brynn mows 1 11/12 of the lawn per hour.
To find how long it will take to mow the entire lawn, we can set up a proportion using the unit rate:
(1 11/12) / (1 hour) = (entire lawn) / (x hours)
Cross-multiplying, we get:
(1 11/12) * (x hours) = 1 * (entire lawn)
Simplifying the left side:
23/12 * x = entire lawn
To find the value of x, we need to divide both sides by 23/12:
x = (entire lawn) / (23/12)
Since the unit rate is given as 1 11/12, it will take 1 11/12 hours to mow the entire lawn.