It takes Shawn 2 more hours to stain a deck than Michelle. Together it takes them 2.4 hours to complete the work. How long would it take Shawn to stain the deck by himself?

Answer: 6 hours

Step-by-step 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