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Loc can mow his entire lawn in 20 minutes; Loc's roommate Reza needs 30 minutes to mow the entire lawn. If Loc starts mowing at 1:00, mows for five minutes and then Reza starts to help with his own mower, at what time will they finish mowing the lawn? Express your answer in the form h:mm.



Answer :

[tex]Loc:\\entire\ lawn\ in\ 20min\\\frac{1}{20}\ lawn\ in\ 1min\\\\Reza:\\entire\ lawn\ in\ 30min\\\frac{1}{30}\ lawn\ in\ 1min\\\\Loc\ and\ Reza\ together:\\\frac{1}{20}+\frac{1}{30}=\frac{3}{60}+\frac{2}{60}=\frac{5}{60}=\frac{1}{12}\ lawn\ in\ 1min\\-----------------------\\Loc\ mows\ for\ 5\ min,\ 5\times\frac{1}{20}=\frac{1}{4}\ lawn\\------------------------[/tex]

[tex]Loc\ and\ Reza\ together\ the\ rest\ of\ the\ lawn\ (\frac{3}{4})\ in\ "t"\ time:\\\frac{1}{12}t=\frac{3}{4}\ \ \ \ \ |multiply\ both\ sides\ by\ 12\\\\t=3\times3\\\\t=9\ (min)\\------------------\\5min+9min=14min\\\\\boxed{Answer:At\ 1:14.}[/tex]
kate200468
[tex]x\ \rightarrow\ \ \ time\ of\ mowing\ of\ lawn \\\\ \frac{20-5}{20} =( \frac{1}{20} + \frac{1}{30} )\cdot (x-5)\\\\ \frac{15}{20} = \frac{3+2}{60}\cdot (x-5)\\\\ \frac{3}{4} = \frac{5}{60} \cdot (x-5)\\\\ \frac{3}{4} = \frac{1}{12} (x-5)\ /\cdot12\\\\ \frac{3}{4} \cdot12=x-5\\\\9=x-5\ \ \ \Rightarrow\ \ \ x=14\ (minutes)\\\\Ans.\ Lok\ and\ Reza\ finish\ mowing\ the\ lawn\ at\ 1:14[/tex]

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