Identify the constant of proportionality (unit rate) for the following :
Josh mows 1/3 acre in 5/6 hour.
(1/3)/(5/6) = x/1
(5/6)x = 1/3
x = (1/3) / (5/6)
x = (1/3) * (6/5)
x = 6/15 = 2/5
He can mow 2/5 of an acre in 1 hour.
To identify the constant of proportionality (unit rate) for the given scenario, we need to determine how much area Josh mows in one hour.
First, let's convert 1/3 acre to the common denominator of 6. Multiply the numerator and denominator by 2 to get 2/6 acre.
Next, we'll divide the area (2/6 acre) by the time (5/6 hour) to find the unit rate. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(2/6 acre) รท (5/6 hour) = (2/6 acre) x (6/5 hour)
Multiplying the numerators (2 x 6) and denominators (6 x 5), we get:
12/30 acre-hour
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6, gives us:
2/5 acre-hour
Therefore, the constant of proportionality (unit rate) for Josh mowing is 2/5 acre per hour.