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. If the three men work together, how long will it take them to complete the job?
Maric's rate = job/8
Hugh's rate = job/6
Ethan's rate = job/12
combined rates = job/8 + job/6 + job/12 = (9/24)job = 9job/24
time to do 1 job = job/( 9job/24 ) = 24/9 = 8/3
it would take 8/3 days
Well, if Maric takes 8 days, Hugh takes 6 days, and Ethan takes 12 days, it seems like Maric is not the quickest bricklayer in town.
But let's focus on teamwork here! Since they are working together, we can't just add up their individual times. Instead, we need to calculate how much work each of them does in a day.
So let's say Maric does 1/8th of the job in one day, Hugh does 1/6th, and Ethan does 1/12th.
When they work together, they combine their efforts and do a total of 1/8 + 1/6 + 1/12 of the job in one day.
To simplify, we can find a common denominator, which is 24. So, 1/8 + 1/6 + 1/12 is the same as (3/24) + (4/24) + (2/24) = 9/24.
This means that together, they are able to complete 9/24 of the job per day.
To find out how long it will take them to complete the job, we can calculate the reciprocal of 9/24, which is 24/9.
Therefore, it will take them approximately 2.67 days to complete the job if they work together. Just make sure they don't crack too many jokes along the way!
To determine how long it will take the three men to complete the job together, we need to calculate the rate at which each person works. The rate at which they work is the reciprocal of the number of days it takes each person to complete the job alone.
Let's calculate the individual rates:
Maric's rate = 1 job / 8 days = 1/8 jobs per day
Hugh's rate = 1 job / 6 days = 1/6 jobs per day
Ethan's rate = 1 job / 12 days = 1/12 jobs per day
To find the combined rate of all three working together, we add up their rates:
Combined rate = Maric's rate + Hugh's rate + Ethan's rate
Combined rate = 1/8 + 1/6 + 1/12
Combined rate = 3/24 + 4/24 + 2/24
Combined rate = 9/24
Now, to find how long it will take them to complete the job together, we calculate the reciprocal of the combined rate:
Time = 1 / Combined rate
Time = 1 / (9/24)
Time = 24/9
Therefore, it will take them approximately 24/9 days to complete the job together. Simplifying the fraction, we get:
Time = 8/3 days
So, it will take them approximately 2.67 days to complete the job together.
To solve this problem, we can use the concept of "work rates".
Let's denote the number of days it takes each person to complete the job working alone as follows:
- Maric: 8 days
- Hugh: 6 days
- Ethan: 12 days
The work rate is inversely proportional to the number of days. So, the work rate of each person can be calculated as the reciprocal of the number of days:
- Maric's Work Rate: 1/8 job per day
- Hugh's Work Rate: 1/6 job per day
- Ethan's Work Rate: 1/12 job per day
Now, if all three men work together, we can find their combined work rate by adding up their individual work rates:
Combined Work Rate = Maric's Work Rate + Hugh's Work Rate + Ethan's Work Rate
Substituting the values we calculated earlier, we have:
Combined Work Rate = 1/8 + 1/6 + 1/12
To simplify, we find a common denominator, which in this case is 24:
Combined Work Rate = (3/24) + (4/24) + (2/24) = 9/24
Now, we divide the total work (1 job in this case) by the combined work rate to find the time it takes for them to complete the job together:
Time Taken = Total Work / Combined Work Rate
Time Taken = 1 / (9/24) = 24/9 = 2.67 days
Therefore, it will take approximately 2.67 days for Maric, Hugh, and Ethan to complete the job together.