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!
