Nitai M. answered • 12/08/19

Experienced High School and College Tutor Specializing in STEM

Javier paints 1 house in 7 hours. This is equivalent to saying that he paints at a rate of 1 house per 7 hours.

Bob paints at an unknown rate of 1 house per **x** hours.

When they paint together, their rates are additive. Therefore, we can say that the sum of their rates,

(1 / 7) + (1 / x), is equal to the given rate of 1 house per 5 hours.

Mathematically, we can write:

(1 / 7) + (1 / x) = (1 / 5), where the denominators have units of "hours" and the numerators are in "houses".

To solve for x, let's create a common denominator on the left by multiplying the first fraction by (x / x) and the second fraction by (7 / 7).

(x / 7x) + (7 / 7x) = (1 / 5)

(7 + x) / (7x) = (1 / 5)

7 + x = 7x / 5

35 + 5x = 7x

35 = 2x

x = 17.5 hours

Hope this helps!