Question

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?

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