Question

Ria can paint a room in 4 hours. Destiny can paint the same room in 6 hours. How long would it take Ria and Destiny to paint the room if they were working together? Provide your answer in decimal form and omit units.

Answer 1

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

$\dfrac{1}{t}.$

Now,

Ria can paint a room in 4 hours. So, in 1 hour, the fraction of the work done by Ria is

$\dfrac{1}{4}$.

Also, Destiny can paint the room in 6 hours. So, in 1 hour, the fraction of teh work done by Destiny is

$\dfrac{1}{6}.$

Therefore, we get

$\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{6}\\\\\\ \Rightarrow \dfrac{1}{t}=\dfrac{3+2}{12}\\\\\\ \Rightarrow \dfrac{1}{t}=\dfrac{5}{12}\\\\\\\Rightarrow t=\dfrac{12}{5}\\\\\\\Rightarrow t=2.4.$

Thus, the required time taken by Ria and Destiny to paint the room together is 2.4 hours.

Answer 2

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,

$\frac{1x}{4}+\frac{1x}{6}=1$

The LCD of 4 and 6 is 12

$\frac{3x+2x}{12}=1$

$\frac{5x}{12}=1$

$5x=12$

$x=\frac{12}{5}$

Hence, both of them can paint the room in $\frac{12}{5}$ hours or 2.4 hours.