Your lawn mower mows a lawn in 1.5 hours. When your friend's lawn mower is used together with your lawn mower, the lawn is mowed in 0.5 hours. How long (in hours) does it take your friend's mower to mow the lawn when working alone?

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Question:

Your lawn mower mows a lawn in 1.5 hours. When your friend's lawn mower is used together with your lawn mower, the lawn is mowed in 0.5 hours. How long (in hours) does it take your friend's mower to mow the lawn when working alone?

Answer:My friend's mower will take approximately 0.75 h to mow the lawn alone.Step-by-step explanation:To solve this problem we can use the idea of average speed and apply to this problem, using the appropriate formula shown below:[tex]speed = \frac{distance}{time}[/tex]Where each lawn mower has a speed at which they can mown, the distance is the lawn they're mowing and the time is how long they will take to do it. In the case where my equipment is working alone, its speed "x" can be modeled as below:[tex]x = \frac{lawn}{1.5}[/tex]When my friend's mower does the job, its speed "y" can be seen as:[tex]y = \frac{lawn}{time}[/tex]When both work together the speed can be seen as:[tex]x + y = \frac{lawn}{0.5}[/tex]Applying the first two equations on the second, gives us:[tex]\frac{lawn}{1.5} + \frac{lawn}{time} = \frac{lawn}{0.5}\\\frac{1}{time} = \frac{1}{0.5} - \frac{1}{1.5}\\\frac{1}{time} = 2 - 0.667\\\frac{1}{time} = 1.333\\1.333*time = 1\\time = \frac{1}{1.333} = 0.75[/tex]My friend's mower will take approximately 0.75 h to mow the lawn alone.

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