Question

max can mow a lawn in 45 minutes. jan takes twice as long to mow the same lawn. if they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together.
\\(\frac{1}{45} + \frac{1}{90} = \frac{1}{t}\\)

how long will it take maxine and jan to mow the lawn together?

\\(\circ\\) 30.0 minutes
\\(\circ\\) 45.0 minutes
\\(\circ\\) 67.5 minutes
\\(\circ\\) 135.0 minutes

Explanation:

Step1: Simplify the left - hand side

First, find a common denominator for \(\frac{1}{45}\) and \(\frac{1}{90}\). The common denominator of 45 and 90 is 90. So we rewrite \(\frac{1}{45}\) as \(\frac{2}{90}\) (because \(45\times2 = 90\) and \(1\times2=2\)). Then \(\frac{1}{45}+\frac{1}{90}=\frac{2}{90}+\frac{1}{90}\).
Adding the numerators, we get \(\frac{2 + 1}{90}=\frac{3}{90}\), and simplifying \(\frac{3}{90}\) gives \(\frac{1}{30}\). So the equation \(\frac{1}{45}+\frac{1}{90}=\frac{1}{t}\) becomes \(\frac{1}{30}=\frac{1}{t}\).

Step2: Solve for t

If \(\frac{1}{30}=\frac{1}{t}\), then by cross - multiplying (since if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)), we have \(t\times1 = 30\times1\), so \(t = 30\).

Answer:

30.0 minutes