Zeno takes 12 min longer to decorate a dozen cupcakes than it takes Lia. When they work​ together, it takes them 17.5 min. How long would each take to do the job​ alone?

Answer 1

1(L+12) + 1/L = 1/17.5

17.5L + 17.5(L+12) = L(L+12)

35L + 210 = L^2 + 12L

L^2 -23L -210 = 0

L= 23/2 + (1/2)sqr(23^2 +840) = 11.5 +.5(37) = 11.5+18.5 =30

L=30 minutes for Lia alone

Z=L+12 = 42 minutes for Zeno alone

on average they do it alone in (30+42)/2 =72/2 = 36 minutes

36/2 = 18 minutes. IF they each did it alone in 36 minutes, together they'd do it in 18 minutes.

17.5 is slightly less than 18.