Question 980198


Let &nbsp;<B>x</B>&nbsp; be the time &nbsp;(in hours)&nbsp; it takes for &nbsp;<B>B</B>&nbsp; to cleans the room.


Then &nbsp;<B>A</B>&nbsp; is cleaning &nbsp;{{{1/5}}}&nbsp; of the room area in &nbsp;1&nbsp; hour, &nbsp;and &nbsp;<B>B</B>&nbsp; is cleaning &nbsp;{{{1/x}}}&nbsp; of the room area in &nbsp;1&nbsp; hour. &nbsp;Working together, &nbsp;they are cleaning &nbsp;{{{1/5}}} + {{{1/x}}}&nbsp; of the room in &nbsp;1&nbsp; hour. 


From the condition, you have an equation 


{{{1/5}}} + {{{1/x}}} = {{{3/5}}},


since after &nbsp;2&nbsp; hours &nbsp;<B>A</B>&nbsp; just cleaned &nbsp;{{{2/5}}}&nbsp; of the room &nbsp;and only &nbsp;{{{3/5}}}&nbsp; remained to clean.


Solve this equation step by step:


x + 5 = 3x, &nbsp;&nbsp;&nbsp;&nbsp;(after multiplying both sides of the equation by &nbsp;5x)

2x = 5,

x = 2.5.


<B>Answer</B>. &nbsp;It will take &nbsp;2{{{1/2}}}&nbsp; hours for &nbsp;<B>B</B>&nbsp; to clean the room working alone.