Answer:
The number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is:
Step-by-step explanation:
To find the answer, first, we're gonna find how many hours take to make the piece of work in 16 days, taking into account each day just has 10 hours:
- Number of hours to make a piece of work = 16 * 10 hours
- Number of hours to make a piece of work = 160 hours.
Now, we divide the total hours among the number of persons:
- Equivalence of hours per person = 160 hours / 80 persons.
- Equivalence of hours per person = 2 hours /person
This equivalence isn't the real work of each person, we only need this value to make the next calculations. Now, we have a piece of work twice as great as the first, then, we can calculate the hours the piece of work needs to perform it (twice!):
- Number of hours to make the second piece of work = 160 hours * 2
- Number of hours to make the second piece of work = 320 hours
We need to make this work in tenth part of the time working 8 hours a day, it means:
- Time used to the second work = 320 hours / 10
- Time used to the second work = 32 hours
- Time used to the second work = 32 hours / 8 hours (as each day has 8 hours)
- Time used to the second work = 4 days
Now, we know three of the second set can do as much work as four of the first set, taking into account the calculated equivalence, we have:
- Work of four workers of first set = Work of three workers of second set
- Work of four workers of first set = Equivalence * 4 persons.
- Work of four workers of first set = 2 hours /person * 4 persons
- Work of four workers of first set = 8 hours.
So, three persons of the second set can make a equivalence of 8 hours. At last, we calculate all the number of workers we need in a regular time:
- Number of needed workers in a regular time = (320 hours / 8 hours) * 3 persons.
- Number of needed workers in a regular time = 40 * 3 persons
- Number of needed workers in a regular time = 120 persons
Remember we need to perform the job not in a regular time, we need to perform it in tenth part of the time, by this reason, we need 10 times the number of people:
- Number of needed workers in tenth part of the time = 120 persons * 10
- <u>Number of needed workers in tenth part of the time = 1200 persons</u>
With this calculations, <em>you can find the number of men needed to perform a piece of work twice as great in tenth part of the time working 8 hours a day supposing that three of the second set can do as much work as four of the first set is </em><u><em>1200 persons</em></u>.
