Question

Sally can paint a room in 8 hours while it takes Steve 3 hours to paint the same room. How long would it take them to paint the room if they worked​ together?

Answer 1

To determine how long it would take Sally and Steve to paint the room if they worked together, we can use the concept of work rates.

Let's denote the time it takes for them to paint the room together as "t" (in hours).

Sally's work rate is 1/8 of the room per hour, since she can paint the room in 8 hours. Steve's work rate is 1/3 of the room per hour, as he can paint the room in 3 hours.

When they work together, their work rates are additive. So, the combined work rate is:

1/8 + 1/3 = 3/24 + 8/24 = 11/24 of the room per hour.

To find the time it takes for them to paint the room together, we can set up the equation:

(11/24) * t = 1

Here, we multiply their combined work rate (11/24) by the time (t) to equal the whole room (1).

To solve for "t," we can multiply both sides of the equation by the reciprocal of (11/24), which is (24/11):

t = (1) * (24/11)

Simplifying the right side, we have:

t = 24/11

Therefore, it would take them approximately 2.18 hours (or about 2 hours and 11 minutes) to paint the room if they worked together.

Answer 2

To find out how long it would take Sally and Steve to paint the room together, you can use the concept of their work rates.

Sally can paint a room in 8 hours, which means she can complete 1/8 of the room's painting work in one hour.

Steve can paint the same room in 3 hours, which means he can complete 1/3 of the room's painting work in one hour.

When they work together, their work rates add up:

Sally's work rate + Steve's work rate = (1/8) + (1/3)

Now, find a common denominator, which is 24:

(3/24) + (8/24) = 11/24

So, when Sally and Steve work together, they can complete 11/24 of the room's painting work in one hour.

To find out how long it will take them to paint the whole room together, take the reciprocal of this combined work rate:

1 / (11/24) = 24/11

So, it will take them approximately 2.18 hours (rounded to the nearest hundredth) to paint the room together.