Question 914657
Let {{{ x }}} = the fraction of the job they get
done while working together
----------------------------
Let {{{ t }}} = time for assistant to finish 
the job working alone
--------------------
(1) {{{ 1/12 + 1/t = x/4 }}}
--------------------
Equation for the assistant working alone:
(2) {{{ 1/t = (( 1-x )) / 10 }}}
--------------------
Multiply both sides of (1) by {{{ 12t }}}
(1) {{{ t + 12 = 3t*x }}}
(1) {{{ x = 1/3 + 4/t }}}
---------------------
Multiply both sides of (2) by {{{ 10t }}}
(2) {{{ 10 = t*( 1-x ) }}}
(2) {{{ 10 = t - t*x }}}
(2) {{{ t*x = t - 10 }}}
(2) {{{ x = 1 - 10/t }}}
---------------------
Set (1)  = (2)
{{{ 1/3 + 4/t = 1 - 10/t }}}
{{{ (( 4 + 10 )) / t = 1 - 1/3 }}}
{{{ 14/t = 2/3 }}}
{{{ 42 = 2t }}}
{{{ t = 21 }}}
------------
The assistant working alone
takes 21 hrs
------------
check:
(1) {{{ 1/12 + 1/t = x/4 }}}
(1) {{{ 1/12 + 1/21 = x/4 }}}
Multiply both sides by {{{ 84 }}}
(1) {{{ 7 + 4 = 21x }}}
(1) {{{ x = 11/21 }}}
That means:
{{{ 1 - x = 10/21 }}}
-----------------
(2) {{{ 1/t = (( 1-x )) / 10 }}}
(2) {{{ 1/21 = ((10/21)) / 10 }}}
Multiply both sides by {{{ 210 }}}
(2) {{{ 10 = 10 }}}
OK
Hope I got it