Sarah can paint a small room in 45 minutes. Sam can paint that same room in 20 minutes. If they work together, how long will it take them to paint the room?

Question

I seriously need help, I don't understand this at all and it says show all work so I know I'm screwed, Help Please?

Answer 1

Our first goal is to figure out how much of the room each person can paint in one minute. This is the rate at which they paint.

 

Sarah paints 1 room per 45 minutes, which means she paints at a rate of 1/45 room per minute. Sarah paints 1/45 of the room every minute.

 

Sam paints 1 room per 20 minutes, which means he paints at a rate of 1/20 room per minute. Sam paints 1/20 of the room every minute.

 

 

 

Our next goal is to figure out how much of the room the two can paint together in one minute. This is their combined rate of painting.

 

Every minute, Sarah paints 1/45 of the room and Sam paints 1/20 of the room. Their combined rate is:

 

1/45 + 1/20 = 4/180 + 9/180 = 13/180

 

Together, Sarah and Sam paint 13/180 of the room every minute.

 

 

 

Finally, we can use their combined rate to find out how long it will take to paint the whole room. They paint at a rate of 13/180 of the room per minute. We want to know how many minutes x it will take for them to paint all 180/180 of the room. So:

 

(13/180)x = 180/180

(13/180)x = 1

13x = 180

x = 180/13

 

Together, Sarah and Sam can paint the room in x = 180/13 ≈ 13.85 minutes.