Question

alan mows lawns in the summer to make money. he knows that, on average, he can mow\\(\frac{1}{2}\\) of a lawn in\\(1\frac{1}{4}\\) hours. calculate his average mowing rate in lawns per hour. \\(\frac{1}{3}\\) lawns per hour \\(2\frac{1}{2}\\) lawns per hour \\(\frac{2}{5}\\) lawns per hour 2 lawns per hour question 14 (5 points)

Explanation:

Step1: Recall the rate formula

Rate is defined as the amount of work done divided by the time taken. Here, the work is mowing lawns, so the rate \( r \) (in lawns per hour) is given by \( r=\frac{\text{Number of lawns mowed}}{\text{Time taken}} \).

Step2: Identify the values

The number of lawns mowed is \( \frac{1}{2} \) lawn, and the time taken is \( 1\frac{1}{4} \) hours. First, convert \( 1\frac{1}{4} \) to an improper fraction. \( 1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4} \) hours.

Step3: Calculate the rate

Substitute the values into the rate formula: \( r=\frac{\frac{1}{2}}{\frac{5}{4}} \). When dividing by a fraction, we multiply by its reciprocal, so \( r=\frac{1}{2}\times\frac{4}{5} \).

Step4: Simplify the multiplication

Multiply the numerators and denominators: \( \frac{1\times4}{2\times5}=\frac{4}{10}=\frac{2}{5} \).

Answer:

\(\frac{2}{5}\) lawns per hour (corresponding to the option: \(\frac{2}{5}\) lawns per hour)