Question

Sally can paint a room in 5 hours while it takes Steve 7 hours to paint the same room. How long will it take them to paint the room if they work together?
(Type an integer or decimal rounded to one decimal place as needed)

Answer 1

Answer:  2.9 hours approximately

=====================================================

Explanation:

Let's say the room has walls and ceiling of 350 sq ft in total area.

Sally can paint this area in 5 hours when working alone, so her unit rate is 350/5 = 70 sq ft per hour.

Steve needs 7 hours to do the same job when working alone, so his unit rate is 350/7 = 50 sq ft per hour.

Assuming the two people can work together without hindering each other (i.e. without getting in each other's way), then the two unit rates combine to 70+50 = 120 sq ft per hour.

Divide the total area over this combined unit rate

350/120 = 2.91667 approximately

This rounds to 2.9

--------------

Alternatively, you can solve the equation

$\frac{1}{5} + \frac{1}{7} = \frac{1}{x}$

And you should get roughly x = 2.9