Work Problems - Easy 1

Let $t$ be the total time in hours to finish the painting job if they work together. The fractional part of the work which Mr. McCartney does in one hour is $\dfrac{1}{10}$ , and for the hired painter is $\dfrac{1}{6}$ . Since they finish the job, then we have

$t\left(\dfrac{1}{10}\right) + t\left(\dfrac{1}{6}\right) = 1$

It follows that $t=3.75~\text{hours}$ .

$\large t\left(\dfrac{1}{10} \right)+t\left(\dfrac{1}{6}\right)=1$

$\large t\left(\dfrac{1}{10} +\dfrac{1}{6}\right)=1$

$\large \boxed{t=3.75}$

let r be amount of paint work. Then Mr. McCartney working speed is r/10 and that of hired worker is r/6. Let t be the amount of time they worked together.So we have (r/10)x t + (r/6)x t=r which gives t=30/8=3.75

Imagine if they were working for 60 hours, Mr McCartney would have painted 6 rooms while the hired painter could finish 10 rooms. So in 60 hours they both managed to paint 16 rooms.Then for 1 room, they could finish in 60/ 16 hours.

The equation is

$\frac {xy}{x+y}$ = $\text{number of total hours if worked together}$

$10$ and $6$ hours represent as $x$ and $y$ , so

$\frac {(10)(6)}{10+6} = \frac {60}{16} = 3.75$

so $\boxed{3.75}$ is the total number of hours they can finish painting the room if they worked together.