Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work
alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would
take him 6 days to complete and if Ethan were to work by himself, the job would take him
12 days to complete. What fraction of the house will each bricklayer complete.
To find the fraction of the house completed by each bricklayer, we need to compare the amount of work done by each bricklayer when they work alone.
Maric can complete the job in 8 days, so in 1 day he completes 1/8th of the job.
Hugh can complete the job in 6 days, so in 1 day he completes 1/6th of the job.
Ethan can complete the job in 12 days, so in 1 day he completes 1/12th of the job.
To find the fraction of the job completed by each bricklayer, we can add up their daily rates:
Maric: 1/8
Hugh: 1/6
Ethan: 1/12
Adding the fractions, we have:
1/8 + 1/6 + 1/12 = 3/24 + 4/24 + 2/24 = 9/24 = 3/8
Therefore, each bricklayer completes 3/8ths of the house.
To determine the fraction of the house each bricklayer will complete, we need to consider the amount of work each bricklayer can do in one day.
Let's start by calculating the rate at which each bricklayer works:
- Maric takes 8 days to complete the job, so his daily rate is 1/8 of the house.
- Hugh takes 6 days to complete the job, so his daily rate is 1/6 of the house.
- Ethan takes 12 days to complete the job, so his daily rate is 1/12 of the house.
Now we can calculate the fraction of the house each bricklayer will complete by multiplying their daily rate by the number of days they work:
- Maric works alone for the entire job, so he will complete 1/8 of the house.
- Hugh works alone for the entire job, so he will complete 1/6 of the house.
- Ethan works alone for the entire job, so he will complete 1/12 of the house.
Therefore, the fraction of the house each bricklayer will complete is as follows:
- Maric: 1/8
- Hugh: 1/6
- Ethan: 1/12