A man can do a certain task in 21 hours, another man can do the task in 28 hours and a boy can do the task in 48 hours. Find how long it will take to do the task if all three work.
You've already posted the exact same question, to which I replied.
You also posted an earlier, similar question, which was answered. Did you not learn from the process on the other question?
they each do a fraction of the task, based on their individual times ... the fractions sum to one (the whole task)
t/21 + t/28 + t/48 = 1 ... LCD is ... 21 * 16
16t/336 + 12t/336 + 7t/336 = 336/336
35t = 336
noted
To find out how long it will take for all three individuals to complete the task together, we need to calculate their combined efficiency.
The efficiency of a person is typically measured as the reciprocal of the time taken to complete the task. For example, if a person takes 10 hours to complete a task, their efficiency would be 1/10th or 0.1 (since it's the reciprocal).
So, let's calculate the individual efficiencies:
The first man's efficiency = 1/21 (as he takes 21 hours to complete the task)
The second man's efficiency = 1/28 (as he takes 28 hours to complete the task)
The boy's efficiency = 1/48 (as he takes 48 hours to complete the task)
Now, to find the combined efficiency, we simply add up their individual efficiencies:
Combined efficiency = 1/21 + 1/28 + 1/48
To simplify this fraction, you can find the least common multiple (LCM) of 21, 28, and 48, which is 336. Then, multiply each fraction by the appropriate factor to have a common denominator of 336:
1/21 x (16/16) = 16/336
1/28 x (12/12) = 12/336
1/48 x (7/7) = 7/336
Now, add up the fractions:
Combined efficiency = 16/336 + 12/336 + 7/336
= 35/336
This gives us the combined efficiency of the three individuals working together.
To find out how long it will take them to complete the task together, we need to take the reciprocal of the combined efficiency:
Time taken = 1 / (35/336)
Taking the reciprocal of a fraction is equivalent to flipping the numerator and denominator:
Time taken = 336/35
Now, simplify the fraction:
Time taken = 9.6 hours (rounded to one decimal place)
Therefore, if all three individuals work together, it will take them approximately 9.6 hours to complete the task.