Respuesta :
Time taken by Ria to paint a room = 4 hours
Time taken by Destiny to paint a room = 6 hours
If they work together, they complete 1 job. So,
[tex]\frac{1x}{4}+\frac{1x}{6}=1[/tex]
The LCD of 4 and 6 is 12
[tex]\frac{3x+2x}{12}=1[/tex]
[tex]\frac{5x}{12}=1[/tex]
[tex]5x=12[/tex]
[tex]x=\frac{12}{5}[/tex]
Hence, both of them can paint the room in [tex]\frac{12}{5}[/tex] hours or 2.4 hours.
Answer: The required time taken by Ria and Destiny to paint the room together is 2.4.
Step-by-step explanation: Given that Ria can paint a room in 4 hours. Destiny can paint the same room in 6 hours.
We are to find the time to paint the room if Ria and Destiny work together.
Let t hours be the time taken to paint the room by Ria and Destiny if they work together.
So, in 1 hour, the fraction of the work done by Ria and Destiny is
[tex]\dfrac{1}{t}.[/tex]
Now,
Ria can paint a room in 4 hours. So, in 1 hour, the fraction of the work done by Ria is
[tex]\dfrac{1}{4}[/tex].
Also, Destiny can paint the room in 6 hours. So, in 1 hour, the fraction of teh work done by Destiny is
[tex]\dfrac{1}{6}.[/tex]
Therefore, we get
[tex]\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{6}\\\\\\ \Rightarrow \dfrac{1}{t}=\dfrac{3+2}{12}\\\\\\ \Rightarrow \dfrac{1}{t}=\dfrac{5}{12}\\\\\\\Rightarrow t=\dfrac{12}{5}\\\\\\\Rightarrow t=2.4.[/tex]
Thus, the required time taken by Ria and Destiny to paint the room together is 2.4 hours.
