Question

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 1

`x\ \rightarrow\ \ \ time\ of\ mowing\ of\ lawn \\\\ (20-5)/(20) =( (1)/(20) + (1)/(30) )\cdot (x-5)\\\\ (15)/(20) = (3+2)/(60)\cdot (x-5)\\\\ (3)/(4) = (5)/(60) \cdot (x-5)\\\\ (3)/(4) = (1)/(12) (x-5)\ /\cdot12\\\\ (3)/(4) \cdot12=x-5\\\\9=x-5\ \ \ \Rightarrow\ \ \ x=14\ (minutes)\\\\Ans.\ Lok\ and\ Reza\ finish\ mowing\ the\ lawn\ at\ 1:14`

Answer 2

`Loc:\\entire\ lawn\ in\ 20min\\(1)/(20)\ lawn\ in\ 1min\\\\Reza:\\entire\ lawn\ in\ 30min\\(1)/(30)\ lawn\ in\ 1min\\\\Loc\ and\ Reza\ together:\\(1)/(20)+(1)/(30)=(3)/(60)+(2)/(60)=(5)/(60)=(1)/(12)\ lawn\ in\ 1min\\-----------------------\\Loc\ mows\ for\ 5\ min,\ 5*(1)/(20)=(1)/(4)\ lawn\\------------------------`


`Loc\ and\ Reza\ together\ the\ rest\ of\ the\ lawn\ ((3)/(4))\ in\`