Question 691561
Jose and Carl together can retile a roof in 10 hours.
 Working alone, Jose could do the job 4.5 hours faster than Carl.
 How long would each man need to work to do the job himself?
:
Let j = Jose's time to do the job
then
(j+4.5) = Carl's time
:
Let the competed job = 1
:
{{{10/j}}} + {{{10/((j+4.5))}}} = 1
multiply by j(j+4.5) to clear the denominators, results:
10(j+4.5) + 10j = j(j+4.5)
10j + 45 + 10j = j^2 + 4.5j
A quadratic equation
0 = j^2 + 4.5j - 20j -45
j^2 - 15.5j - 45 = 0
:
solve this, the positive solution; j = 18 hrs