I'm confused on how to find the equation.

Question

The Turtledove Chocolate factory has two chocolate machines. Machine A takes s minutes to fill a case, and machine B takes s + 10 minutes to fill a case. Working together, the two machines take 15 minutes to fill a case. Approximately how long does each machine take to fill a case?

Answer 1

1/s + 1/(s+10) = 1/15

eliminate fractions by multiplying by 15s(s+10)

15(s+10) + 15s = s(s+10)

15s + 150 + 15s = s^2 + 10s

(15+15-10)s = s^2 -150

s^2 -20s -150 = 0

s= 20/2 + or - (1/2)sqr(400+600) = 10+ or- 5sqr10

s = 10+5sqr10 (ignore the negative square root)

s= 10 + 15.81 = 25.81 minutes working alone

s+10 = 35.81 minutes working alone

working together = 15 minutes

1/25.81 + 1/35.81 = .039 +.028 = .067 = 1/15

since together they do it in 15 minutes

if they worked at the same speed, they'd each do it in twice the time or 30 minutes alone. but one does it 10 minutes faster, so take 10/2 =5 and add and subtract 5 from 30 to get 25 and 35, which is virtually the exact answer, very close to 25.81 and 35.81