<PRE><B>Question 579917</B>
Fred can paint a certain room in 5 hours.
 One day Fred decides to help his friend Jack paint such a room.
 After they work together for 2 hours Fred goes home and leaves Jack to finish painting the room.
 Jack requires 4 more hours to finish the room.
 How long would it have taken Jack to paint the room alone?
:
Let j = time required by jack to paint the room alone
let the completed job = 1; (a painted room)
:
From the information given, we know Jack painted for a total of 6 hrs and Fred 2 hrs
:
{{{2/5}}} + {{{6/j}}} = 1
multiply by 5j
5j*{{{2/5}}} + 5j*{{{6/j}}} = 5j
cancel the denominators
2j + 5(6) = 5j
30 = 5j - 2j
30 = 3j
j = {{{30/3}}}
j = 10 hrs for jack to do it alone
;
:
Check this
{{{2/5}}} + {{{6/10}}} =
.4 + .6 = 1</PRE>