SOLUTION: Todd contracted to paint a house for $480. It took him 4 hours longer than he anticipated, so he earned $0.50 less per hour than he originally calculated. How long had he anticipat

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Todd contracted to paint a house for $480. It took him 4 hours longer than he anticipated, so he earned $0.50 less per hour than he originally calculated. How long had he anticipat      Log On


   

Question 503630: Todd contracted to paint a house for $480. It took him 4 hours longer than he anticipated, so he earned $0.50 less per hour than he originally calculated. How long had he anticipated it would take him to paint the house?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Todd contracted to paint a house for $480. It took him 4 hours longer than he anticipated, so he earned $0.50 less per hour than he originally calculated.
How long had he anticipated it would take him to paint the house?
:
Let t = no. of hr he anticipated to paint the house
then
(t+4) = no. of hrs he actually required to paint the house
:
480%2Ft = the hourly pay he anticipated
:
480%2Ft - 480%2F%28%28t%2B4%29%29 = .50
multiply by t(t+4), results
480(t+4) - 480t = .5t(t+4)
480t + 1920 - 480t = .5t^2 + 2t
1920 = .5t^2 + 2t
A quadratic equation
.5t^2 + 2t - 1920 = 0
Multiply by 2 to give t^2 a coefficient of 1
t^2 + 4t - 3840 = 0
You can use the quadratic formula to find t, however this will factor to:
(t+64)(t-60) = 0
the positive solution
t = 60 hrs he anticipated to paint the House
:
:
Confirm this by finding the actual hourly pair
480/64 = $7.50, actual pay
480/60 = $8.00, hoped for pay