Question

15) Noah and Owen paint houses together. If Noah can paint a particular house in 6 days and Owen

can paint the same house in 5 days. How long will it take them to paint the house together?
a) Define the variable.
b) Create a rational equation.
c) Solve the rational equation for how long in days it will take them to paint the house together,

Answer 1

It’ll take 3 days to paint the house together

Answer 2

1/6 + 1/5 = 1/x, 3 days

Explanation:

a) x days will take to paint the house together.

b) 1/6 part of the house, Noah paints for 1 day.

1/5 part of the house, Owen paints for 1 day

1/x part of the house they paint for 1 day together, and also we can write that

(1/6 + 1/5) part of the house they paint for 1 day together.

So, we can write equation

1/6 + 1/5 = 1/x

c) 1/6 + 1/5 = 1/x

30x*1/6 + 30x*1/5 = 30x*1/x

5x + 6x = 30

11x = 30

x = 30/11 ≈2.72 ≈ 3 days