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
[tex] \frac{1}{4} [/tex]
Also, if James can do it in 5 hours, then his working rate is
[tex] \frac{1}{5} [/tex]
Let
[tex]x[/tex]
be the hours that both will use to complete the sales route,
Then rate at which both completes this task is
[tex] \frac{1}{x} [/tex]
Meaning if we add their individual rates we should get
[tex] \frac{1}{x} [/tex]
That is;
[tex] \frac{1}{4} + \frac{1}{5} = \frac{1}{x} [/tex]
The LCM is
[tex]20x[/tex]
So let us multiply through with the LCM.
[tex]20x \times \frac{1}{4} + 20x \times \frac{1}{5} =20x \times \frac{1}{x} [/tex]
[tex]5x + 4x = 20[/tex]
We simplify to get,
[tex]9x = 20[/tex]
Dividing through by 9 gives;
[tex]x = \frac{20}{9} [/tex]
[tex]x = 2\frac{1}{9} [/tex]
Therefore the two will complete sales route in
[tex]2 \frac{1}{9} [/tex]
hours.
