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

`(1)/(t).`

Now,

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

`(1)/(4)`.

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

`(1)/(6).`

Therefore, we get

`(1)/(t)=(1)/(4)+(1)/(6)\\\\\\ \Rightarrow (1)/(t)=(3+2)/(12)\\\\\\ \Rightarrow (1)/(t)=(5)/(12)\\\\\\\Rightarrow t=(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,

`(1x)/(4)+(1x)/(6)=1`

The LCD of 4 and 6 is 12

`(3x+2x)/(12)=1`

`(5x)/(12)=1`

`5x=12`

`x=(12)/(5)`

Hence, both of them can paint the room in
`(12)/(5)` hours or 2.4 hours.