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?\
67.5 minutes\
45.0 minutes\
30.0 minutes\
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 \(\frac{2}{90}\). Then \(\frac{1}{45}+\frac{1}{90}=\frac{2}{90}+\frac{1}{90}=\frac{2 + 1}{90}=\frac{3}{90}=\frac{1}{30}\).

Step2: Solve for \(t\)

We have the equation \(\frac{1}{30}=\frac{1}{t}\). By cross - multiplying (since if \(\frac{a}{b}=\frac{c}{d}\), then \(ad = bc\)), we get \(t\times1=30\times1\), so \(t = 30\).

Answer:

30.0 minutes