Answer: 6 hours
Explanation:
Shawn's time = Ts
Michele's time = Tm
But Tm + 2hours = Ts
Time here is expressed according to work done, their time rate of work can be given by:
r = Wd/T (where r is the rate of work per time, Wd is work done and T is time spent)
Since the amount of work is the same for both of them, their rate of work together is given by
Wd/Tt = Wd/Tm + Wd/Ts
Since Wd is the same across board, we can eliminate Wd, leaving us with:
1/Tt = 1/Tm + 1/Ts (Tt represents the time they both expended in doing the work together
Tt = 2.4 hours
Therefore,
1/2.4= 1/Tm + 1/Ts
Taking the LCM of the left hand side fraction
1/2.4 = (Ts + Tm)/TmTs
We cross multiply
2.4Ts + 2.4Tm = TmTs........
Remember, Ts = (Tm + 2)hrs
We substitute for Ts
2.4(Tm + 2) + 2.4Tm = Tm(Tm +2)
2.4Tm + 4.8 + 2.4Tm = Tm2 + 2Tm
4.8Tm + 4.8 = Tm2 + 2Tm
Tm2 - 2.8Tm - 4.8 = 0
This has become a quadratic equation
We multiply thought by 10 to make factorization easier
10Tm2 - 28Tm - 48 = 0
Then we factorize
(Tm - 4) (10Tm +12) = 0
Tm-4= 0, Tm = 4hours
(The other equation (10Tm+ 12 = 0) will give a negative result for time, we discard it because it is impossible in these circumstances. We all know that time is a scalar quantity)
Tm= 4hours (that is Michelle's time)
Since Tm + 2 = Ts
(4+2)hours = Ts
Ts = 6 hours
Therefore, Shawn will spend 6 hours staining the deck all alone