A painter can finish painting a house in 5 hours. Her assistant takes 7 hours to finish the same job. How long would it take for them to complete the job if they were working together?

Answer 1

Hello Kk O! In order to answer this question, we shall use this equation: (amount of work) = (rate) * (time).

The amount of work (let's use the variable D here) is the same for both the painter and assistant. Because the painter took 5 hours to paint it at a rate P, the equation can be rewritten as D = P * 5. Similarly, the assistant took 7 hours to paint the same house at rate A, so the equation can be written as D = A * 7. To know the time required it takes when working together, we can divide rate by both sides to get:

(amount of work) / (rate) = (time)

When the two work together, that means they accomplish the same D (they are only working on one house), but their rates are adding together. If D = P * 5, then P = D / 5. Similarly, if D = A * 7, then

A = D / 7. So the rearranged equation to find worked-together time T is:

T = D / (P + A) or T = (D) / ( (D / 5) + (D / 7) ), which, after combining the denominator with common denominators, should yield:

T = D / (12 * D / 35), or T = 35 / 12 hours ..... (Answer)

I hope that helped you!