Question 214837
Stuart agrees to a house-painting job for $900.
 He takes 4 days longer than expected,and he has earned $18.75 less per day than expected. 
In how many days did he expect to complete the house?
:
Let t = no. of days expected to paint the house
then
(t+4) = no. of actual days
:
Expected daily pay: {{{900/t}}}
then
Actual daily pay: {{{900/((t+4))}}}
;
Expected daily pay - Actual daily pay  = 18.75
{{{900/t}}} - {{{900/((t+4))}}} = 18.75
Multiply equation by t(t+4), results:
900(t+4) - 900t = 18.75t(t+4)
:
900t + 3600 - 900t = 18.75(t^2 + 4t)
:
900t - 900t + 3600 = 18.75t^2 + 75t
:
Arrange as a quadratic equation
18.75t^2 + 75t - 3600 = 0
:
Simplify, divide by 18.75
t^2 + 4t - 192 = 0
:
(t + 16)(t - 12) = 0
Positive solution
t = 12 days is original no. of days