Question 452654
Sam takes 6 days less than the number of days taken by John to complete a piece of work.
 If both Sam and John together can complete the same work in 4 days.
 In how many days will john complete the work?
:
Let t = time required by John working alone
then
(t-6) = time required by Sam to do this
:
Let the competed job = 1
:
A typical shared work equation
;
{{{4/((t-6))}}} + {{{4/t}}} = 1
multiply by t(t-6)
t(t-6)*{{{4/((t-6))}}} + t(t-6)*{{{4/t}}} = t(t-6)1
:
cancel the denominators, results:
4t + 4(t-6) = t(t-6)
:
4t + 4t - 24 = t^2 - 6t
:
8t - 24 = t^2 - 6t
Combine like terms on the right
0 = t^2 - 6t - 8t + 24
A quadratic equation
t^2 - 14t + 24 = 0
Factors to
(t-2)(t-12) = 0
t = 2
t = 12 days is the reasonable answer for John's time alone
:
:
Check
{{{4/12}}} + {{{4/6}}} = 
{{{1/3}}} + {{{2/3}}} = 1