Question

Sally can paint a room in 4 hours while it takes steve 9 hours to paint the same room. how long would it take them to paint the room if they worked​ together

Answer 1

To find the time it takes for Sally and Steve to paint the room together, we can calculate their combined work rate and take the reciprocal.

Step-by-step explanation:

To solve this problem, we can use the concept of work rates. Sally can paint the room in 4 hours, which means she can paint 1/4 of the room in 1 hour. Similarly, Steve can paint the room in 9 hours, so he can paint 1/9 of the room in 1 hour. When they work together, their work rates add up.

Sally's work rate: 1/4 of the room per hour
Steve's work rate: 1/9 of the room per hour
Combined work rate: 1/4 + 1/9
To find the time it takes for them to paint the room together, we can take the reciprocal of the combined work rate. This gives us the equation:

1 / (1/4 + 1/9) = 1 / (9/36 + 4/36) = 1 / (13/36) = 36/13 hours

Therefore, it would take them approximately 2.77 hours, or 2 hours and 46 minutes, to paint the room together.

Answer 2

Sally ⇒
4 hours = 1 room
1 hour = 1/4 of the room

Steve ⇒
9 hours = 1 room
1 hour = 1/9 of the room

Sally + Steve ⇒
1 hour = 1/4 + 1/9 = 9/36 + 4/36 = 13/36

Number of hours needed ⇒
1 ÷ 13/36 = 1 x 36/13 = 36/13 = 2 10/13 hours

Answer: They need 2 10/13 hours.