SOLUTION: 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 j

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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
;
+ = 1
multiply by t(t-6)
t(t-6)* + t(t-6)* = 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
+ =
+ = 1
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