Problema Solution

John and Dwight can clean an entire building in 2 hours. John can clean the entire building by himself in 3 fewer hours than Dwight can. How long does it take John to clean the building by​ himself?

Answer provided by our tutors

Let

x = the number of hours Dwight needs to clean the building alone

1/x building per hour is Dwight's rate

x - 3 = the number of hours John needs to clean the building alone, x - 3 >0, x > 3

1/(x - 3) building per hour is John's rate

1/2 building per hour is the together rate

Now we can write the equation:

1/x + 1/(x - 3) = 1/2

........

click here to see the equation solved for x

........

x = 6 hr

We need to ignore the solution x = 1 since x > 3.

x - 3 = 6 - 3 = 3 hr

John needs 3 hours to clean the building by himself.