<PRE><B>Question 389489</B>
t takes Jonathan 2/3 as long as it takes Juancho to paint a car.
 If together Jonathan and Juancho take 12 hrs, how long would it take Juancho to do the work alone? 
:
let x = time required by Ju alone
then
{{{2/3}}}x = time required by Jo alone
:
Let the completed job = 1; (a painted car)
:
{{{12/((2/3)x)}}} + {{{12/x}}} = 1
multiply by {{{2/3}}}x, results:
(12) + {{{2/3}}}(12) = {{{2/3}}}x
12 + 8 = {{{2/3}}}x
20 = {{{2/3}}}x
multiply by 3
3(20) = 2x
2x = 60
x = 30 hrs, Ju alone
:
:
Check solution,
{{{2/3}}}30 = 20 hrs, Jo alone
{{{12/20}}} + {{{12/30}}} = 1
.6 + .4 = 1; confirms our solution</PRE>