Question 271324
Let {{{d}}} = number of days he expected job to take
given:
{{{d + 4}}} = number of days job actually took
-----------------------------------------------
{{{900/(d + 4) = 900/d - 18.75}}}
Multiply both sides by {{{d*(d + 4)}}}
{{{900d = 900*(d + 4) - 18.75*d*(d + 4)}}}
{{{900d = 900d + 3600 - 18.75d^2 - 75d}}}
{{{18.75d^2 + 75d - 3600 = 0}}}
I'll solve with quadratic formula
{{{d = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 18.75}}}
{{{b = 75}}}
{{{c = -3600}}}
{{{d = (-75 +- sqrt( 75^2-4*18.75*(-3600) ))/(2*18.75) }}}
{{{d = (-75 +- sqrt(5625 + 270000 ))/37.5 }}}
{{{d = (-75 +- sqrt(275625))/37.5 }}}
{{{d = (-75 +- 525)/37.5 }}}
{{{d = (-75 + 525)/37.5}}}
{{{d = 12}}}
He expected to complete the house in 12 days
check:
{{{900/(d + 4) = 900/d - 18.75}}}
{{{900/(12 + 4) = 900/12 - 18.75}}}
multiply both sides by {{{12*16}}}
{{{900*12 = 900*16 - 18.75*12*16}}}
{{{10800 = 14400 - 3600}}}
{{{10800 = 10800}}}
OK