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Dave can complete a sales route by himself in 4 hours. James can do the same job in 5 hours. How long will it take them to do it working together?

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We can solve this problem by calculating the individual rate of working and equate it to their total rate of working.

If Dave can complete a sales route in 4 hours, then his working rate is


(1)/(4)

Also, if James can do it in 5 hours, then his working rate is


(1)/(5)

Let

x
be the hours that both will use to complete the sales route,

Then rate at which both completes this task is

(1)/(x)


Meaning if we add their individual rates we should get


(1)/(x)

That is;


(1)/(4) + (1)/(5) = (1)/(x)

The LCM is

20x

So let us multiply through with the LCM.


20x * (1)/(4) + 20x * (1)/(5) =20x * (1)/(x)


5x + 4x = 20

We simplify to get,


9x = 20

Dividing through by 9 gives;


x = (20)/(9)


x = 2(1)/(9)

Therefore the two will complete sales route in

2 (1)/(9)
hours.
User MarcM
by
8.5k points

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