SOLUTION: Sam and Justin together can do a work in 2 days. If they had to work separately, the time taken by Justin to do the work would be more than that of Sam by 3 days. In how many days

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Sam and Justin together can do a work in 2 days. If they had to work separately, the time taken by Justin to do the work would be more than that of Sam by 3 days. In how many days       Log On


   

Question 1186013: Sam and Justin together can do a work in 2 days. If they had to work separately, the time taken by Justin to do the work would be more than that of Sam by 3 days. In how many days cam Justin do the work alone? (Applying quadratic equations)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
              RATE             TIME in Days      JOBS

Sam             1/x               x                1

Justin          1/(x+3)           x+3              1

Together        1/2               2                1


highlight_green%281%2Fx%2B1%2F%28x%2B3%29=1%2F2%29
Solving this will lead to a quadratic equation.

Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Sam and Justin together can do a work in 2 days.
If they had to work separately, the time taken by Justin to do the work would be more than that of Sam by 3 days.
In how many days cam Justin do the work alone? (Applying quadratic equations)
~~~~~~~~~~~~~~~~~~~~ 

Sam = x days

Justin = (x+3) days.


The combined rate equation is


    1%2Fx + 1%2F%28x%2B3%29 = 1%2F2.


The solution can be easily guessed MENTALLY:  x = 3 days.


ANSWER.  Sam can complete this job in 3 days, working alone.

         Justin can complete this job in 3+3 = 6 days, working alone.


CHECK.  1%2F3 + 1%2F%283%2B3%29 = 1%2F3+%2B+1%2F6 = 2%2F6+%2B+1%2F6 = 3%2F6 = 1%2F2.    ! Correct !

Solved.

Alternatively,  you can reduce equation  (1)  to the standard quadratic equation form
and solve it formally  EITHER  using the quadratic formula  OR  by factoring.


//////////////


To see other similar solved problems, look into the lesson
    - Using quadratic equations to solve word problems on joint work
in this site.