Question 492733
Doy and his son can do a job in 4 1/2 days, 
After they have worked for 3 days, Doy got sick and the son finished the task in 6 more days.
 How many days each required to do the entire task?
:
Let d = D's working time alone to do the job
Let s = son's working time to do it
Let the completed job = 1
:
"Doy and his son can do a job in 4 1/2 days," therefore
{{{4.5/d}}} + {{{4.5/s}}} = 1
:
From the given information, we know that the son worked a total 9 days
:
{{{3/d}}} + {{{9/s}}} = 1
:
Multiply the 1st equation by 2, use elimination here
{{{9/d}}} + {{{9/s}}} = 2
{{{3/d}}} + {{{9/s}}} = 1
----------------------------subtraction eliminates s find d
{{{6/d}}} = 1
multiply both sides by d
d = 6 days for D to do the job alone
:
Find s
{{{3/6}}} + {{{9/s}}} = 1
multiply by 6s, results:
3s + 6(9) = 6s
54 = 6s - 3s
54 = 3s
s = {{{54/3}}}
s = 18 days for the son to do the job alone
:
:
We can check these solutions in the 1st equation
{{{4.5/6}}} + {{{4.5/18}}} =
.75 + .25 = 1