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Lubov Fominskaja [6]
3 years ago
12

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?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
3 0
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

\frac{1}{4}

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

\frac{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
\frac{1}{x}


Meaning if we add their individual rates we should get

\frac{1}{x}

That is;

\frac{1}{4} + \frac{1}{5} = \frac{1}{x}

The LCM is
20x

So let us multiply through with the LCM.

20x \times \frac{1}{4} + 20x \times \frac{1}{5} =20x \times \frac{1}{x}

5x + 4x = 20

We simplify to get,

9x = 20

Dividing through by 9 gives;

x = \frac{20}{9}

x = 2\frac{1}{9}

Therefore the two will complete sales route in
2 \frac{1}{9}
hours.
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