Respuesta :
Bill paints 1/2 per hour. Bob paints 1/3 per hour. 1/2x+1/3x=1
The time it will take Bob and Bill to paint the closet together is 1.2 hours.
How are number of people to time needed to complete a task related?
More people to do a task means less time it will take.
Less people to do a task means more time it will take.
Thus, they are inversely related.
We can define a constant as "Manpower" needed for doing that specific work.
For this case, we're specified that:
- Work is: painting a considered closet.
- Bill can paint it in 2 hours.
- Bob can paint it in 3 hours.
Manpower needed for painting the closet must be constant.
Let manpower that Bill delivers is x units per hour.
Then in 2 hours, he delivers 2x units of manpower.
Similarly, if we take manpower delivered by Bob as of y units per hour, then in 3 hours, he delivers 3y units of manpower.
2x manpower = manpower needed to paint the closet = 3y manpower.
Thus, we get:
[tex]2x = 3y\\[/tex]
Now, when Bill and Bob will work together, that means, there will be delivery of x + y manpower per hour.
Since 2x = 3y, therefore y = 2x/3
Putting this, we get: [tex]x+y = x + 2x/3 = \dfrac{5x}{3}[/tex]
Let it takes 'h' hours for them together to paint the closet, then:
Manpower for painting closet = [tex]h \times \dfrac{5x}{3}[/tex]
Since it is equal to 2x too, so we get:
[tex]h(\dfrac{5x}{3}) = 2x\\\\\text{Dividing both sides by x}\\\\\dfrac{5h}{3} = 2\\\\5h = 6\\\\h = \dfrac{6}{5} = 1.2 \: \rm hours[/tex]
Thus, the time it will take Bob and Bill to paint the closet together is 1.2 hours.
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