Question

A farmer can do a job on the farm in 6 hours. his older son can do the job in 8 hours. the younger son can do the same job in 12 hours. how long will it take all three to do the job if they work together?

Answer 1

Working together, the farmer, older son, and younger son will take 8/3 hours to complete the job. This is 2 and 2/3 hours or 2 hours and 40 minutes.

To solve this problem, you can use the formula for the combined work rate of multiple individuals working together.

Let the combined work rate of the farmer, older son, and younger son be represented as:

Combined Work Rate= 1/ Time taken by the three together

​The individual work rates are inversely proportional to the time each person takes to do the job. So, the farmer's work rate is 1/6 of the job per hour, the older son's work rate is 1/8 of the job per hour, and the younger son's work rate is 1/ 12 of the job per hour.

To find the combined work rate when they work together:

Combined Work Rate=Farmer’s Work Rate+Older Son’s Work Rate+Younger Son’s Work Rate

Combined Work Rate= 1/6 + 1/8 + 1/ 12

​Now, let's calculate this combined rate:

Combined Work Rate= 4/24 + 3/24 + 2/ 24​ = 9/24​ = 3/8

​This means that together, they can complete 3/8 of the job per hour.

Now, if they're completing 3/8 of the job per hour, it will take them 1/3/8 hours to complete the whole job.

Time taken by the three together=1/3/ 8=8/3

So, working together, the farmer, older son, and younger son will take 8/3 hours to complete the job. This is 2 and 2/3 hours or 2 hours and 40 minutes.