Father can do the job on the farm in 6 hours. The older son can do it in 8 hours. The younger son can do same job in 12 hours. How long will it take them to do the job, if they all work together?

Question

Mathematics

Edgar Odonnell

16 July, 23:20

Father can do the job on the farm in 6 hours. The older son can do it in 8 hours. The younger son can do same job in 12 hours. How long will it take them to do the job, if they all work together?

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Answers (1)

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Natalya Quinn · Answer 1

Answer: it will take a combined rate of 2.67 hours

Step-by-step explanation:

Father can do the job on the farm in 6 hours. This means that the father's unit rate of working will be 1/6

The older son can do it in 8 hours. This means that the older son's rate of working will be 1/8

The younger son can do same job in 12 hours. This means that the younger son's working rate is 1/12

When they work together, they will be working simultaneously. It means that their unit rates are additive. The combined unit rates will be

1/6 + 1/8 + 1/12 = (20 + 15 + 10) / 120

45/120

Assuming it takes t hours for them to complete the work while doing it together. Their combined unit rate will be 1/t

45/120 = 1/t

45t = 120

t = 120/45 = 2.67 hours