Jake can cut and split a cord of firewood in 9 fewer hours than Skyler can. When they work​ together, it takes them 6 hours. How long would it take each of them to do the job​ alone?

Answer 1

1/(s-9) + 1/s = 1/6

multiply by 6s(s-9) to get

6s + 6s-54 = s^2 -9s

s^2 -21s +54 = 0

(s-18)(s-3) =0

s = 3 or 18

s-9 = -6 or 9 ignore the negative answer

s=18 hours for Skylar

s-9 = 9 hours for Jake

they average (18+9)/2 = 27/2 = 13.5

half that = 6.75 hours. Had they each done it alone in 13.5, together they'd do it in 6.75

Jake's faster though so it reduces the time together down to 6 hours.