Potato harvesting

Due to a large potato harvest this year, the farm bought a new, more powerful sorter in addition to the old one. With both machines running simultaneously, the daily harvest is processed in 12 hours. If only the old machine were used, it would need 10 more hours than the new machine to process the daily harvest. How long would the old sorter take on its own?

Final Answer:

a =  30 h

Step-by-step explanation:

T=12 h a = 10+b  T(1/a + 1/b) = 1  T(1/a + 1/(a10)) = 1  T(a10)+T a=(a10) a  12(a10)+12 a=(a10) a a2+34a120=0 a234a+120=0  p=1;q=34;r=120 D=q24pr=34241120=676 D>0  a1,2=2pq±D=234±676 a1,2=234±26 a1,2=17±13 a1=30 a2=4  a>10; a>10h  a=a1=30=30 h  b=a10=3010=20 h

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