<PRE><B>Question 249302</B>
A carpenter and his partner can put up a patio cover in 3 3/7 hours.
 If the partner needs 8 hours to complete the patio alone, how long would it take the carpenter working alone?
:
Let c = time required when carpenter works alone
:
Change 3 3/7 to {{{24/7}}}
Let the completed job = 1
:
A typical shared work equation
{{{(24/7)/c}}} + {{{(24/7)/8}}} = 1
multiply by 8c, results
8{{{(24/7)}}} + c{{{(24/7)}}} = 8c
multiply by 7, results
8(24) + 24c = 7(8c)
:
192 + 24c = 56c
:
192 = 56c - 24c
:
192 = 32c
c = {{{192/32}}}
c = 6 hrs, the carpenter working alone</PRE>