Math question .. need help

[richlittl]

Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?

A.14

B.13

C.11

D.9

E.7

Isn't a "shift" a defined time frame??

[mental]

Total 3 shifts worked per day, with each machine working for 1.5 shifts

Machine A:
2 shifts a day...................12 days to complete the work
1.5 shifts/day...................12*2/1.5 = 16 days to complete the work
in one day it does 1/16 of work

Machine B:
2 shifts a day...................15 days to complete the work
1.5 shifts/day...................15*2/1.5 = 20 days to complete the work
in one day it does 1/20 of work

working together they do 1/16 + 1/20 = 9/80 of work in a day
they complete the work in 80/9 = 9 approx

IMO: D

[stop@800]

I am also getting 80/9
but I think there is no approximate in question so we must be missing something

[mental]

OA please

[richlittl]

D. 9 days