Question 1003593
Let {{{ t }}} = time in hours for the faster
computer to run the program
{{{ t + 16 }}} = time in hours for the 
slower computer to run the program
---------------------------------
Faster computer's rate:
[ 1 program ] / [ t hrs ] = {{{ 1/t }}}
Slower computer's rate:
[ 1 program ] / [ t + 16 hrs ] = {{{ 1/( t+16 ) }}}
-------------------------------------
Let {{{ x }}} = the fraction of the program that
computers get done in 1 hour
Add their rates of computing to get their rate
working together to get:
[ x fraction of program done ] / [ 1 hr] = {{{ x/1 }}}
{{{ 1/t + 1/( t+16 ) = x/1 }}}
--------------------------
The fraction of the job left to do is:
{{{ 1 - x }}}
In the following 14 hours the slower computer
finishes the job, working at the rate:
{{{ ( 1-x ) / 14 }}}, so I can say:
{{{ 1/( t + 16 ) = (( 1 - 1/t - 1/( t+16 ) )) / 14 }}}
{{{ 14/( t + 16 ) = 1 - 1/t - 1/( t+16 ) }}}
{{{ 15/( t + 16 ) = 1 - 1/t }}}
Multiply both sides by {{{ t*( t+16 ) }}}
{{{ 15t = t*( t+16 ) - t - 16 }}}
{{{ 15t = t^2 + 16t - t - 16 }}}
{{{ t^2 = 16 }}}
{{{ t = 4 }}}
The faster computer, working alone, takes 4 hrs
to run the program
------------------
check answer:
{{{ 1/t + 1/( t+16 ) = x/1 }}}
{{{ x = 1/4 + 1/20 }}}
{{{ x = 5/20 + 1/20 }}}
{{{ x = 3/10 }}}
{{{ 1 - x = 7/10 }}}
----------------
{{{ 1/( t + 16 ) = (( 1 - 1/t - 1/( t+16 ) )) / 14 }}}
{{{ 1/20 = ( 7/10 )/14 }}}
{{{ 14/20 = 7/10 }}}
{{{ 7/10 = 7/10 }}}
OK