# Three machines A, B and C are set to work together. A working alone takes 6 hours to complete the work; B takes 8 hours while C takes 12 hours. All the three machines started working at the same time. 40 minutes later machine A broke down. B and C continued for another 1 hour before B ran out of fuel and therefore stopped working for 20 minutes while C continued. If B resumed working after 20 minutes, calculate the:

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Three machines A, B and C are set to work together. A working alone takes 6 hours to complete the work; B takes 8 hours while C takes 12 hours. All the three machines started working at the same time. 40 minutes later machine A broke down. B and C continued for another 1 hour before B ran out of fuel and therefore stopped working for 20 minutes while C continued. If B resumed working after 20 minutes, calculate the:

1. Fraction of the work left after machine A broke down.
2. Fraction of the work done by C working alone for 20 minutes
3. Total time taken for the work to be completed.

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1. 1/6 + 1/8 + 1/12 = 3/8
40/60 x 3/8 = 1/4
= 1 - 1/4 = 3/4

2. 1hr    = 1/12
20min = ?
20/60 x 1/12 = 1/36

3. B & C = 1/8 + 1/125/24
3/4 - 5/24 = 13/2413/24 - 1/36 = 37/72
5/24 = 1hr
37/72 = 37/72 x 24/5 = 27/15
time= 40minutes + 1hr 20 mins + 2hrs 28mins
=4hrs 28min