Question

Sam and you are going to paint your room together.

Sam takes 10 minutes to paint 25 square feet.
It takes you 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take 15
minutes for us to cover 50 square feet."
Give an explanation to convince Sam that she is
incorrect

Answer 1

It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.

Explanation:

The together rate is the sum of the separate rates.

In this question:

Sam's rate is 1/10 for 25 square feet, so 1/20 for 50 square feet.

Your's rate is 1/5 for 25 square feet, so 1/10 for 50 square feet.

Together rate:

`(1)/(x) = (1)/(20) + (1)/(10)`

`(1)/(x) = (1)/(20) + (2)/(20)`

`(1)/(x) = (3)/(20)`

`3x = 20`

`x = (20)/(3) = 6.67`

It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.