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
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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.