Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work​ together?

Question

I got a variation of this this wrong 4 times, need some help.

Answer 1

Assume both delivers work at a constant rate so

W = r₁ t₁ eq (1) and W = r₂ t₂ eq (2),

where W is the work, r_i is the rate of work a deliver does, and t_i is the time it takes the person to finish the job. If they both work together their combined work should equal the total work.

W = r₁ t + r₂ t eq (3)

Substitute eq (1) and (2) into eq (3) to remove r₁ and r₂.

t = W/(r₁ + r₂) = t₁ t₂ /(t₁ + t₂)

t = 30 ⋅ 20 / (20 + 30) minutes= 12 minutes