SOLUTION: 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.

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Question 1103607: 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.
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
a=21 b=28 c=48
1/a+1/b+1/c=1/x
1/21+1/28+1/48=1/x
1344/28224+1008/28224+588/28224=1/x
2940/28224=1/x
28224/2940=x
or 9.6 hours working together
check
1/a+1/b+1/c=1/x
1/21+1/28+1/48=1/9.6
1344/28224+1008/28224+588/28224=1/9.6
2940/28224=1/9.6
28224/2940=9.6
9.6=9.6
ok
codewt3w
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
>>>A man can do a certain task in 21 hours,
So the man's rate in jobs per hour is

1 job per 21 hours or

,

so his rate in jobs/hour is

>>>another man can do the task in 28 hours,
So the other man's rate in jobs per hour is

1 job per 28 hours or

,

so his rate in jobs/hour is

>>>a boy can do the task in 48 hours
That's 1 job per 48 hours or

,

so his rate in jobs/hour is

>>>Find how long it will take to do the task if all three work.
Let x = the number of hours it will take all three to do the task.

Then their combined rate is

1 job per x hours or

,

so their combined rate in jobs/hour is 



Their combined rate is also equal to the sum of their rates, so

Their combined rate = 

So we set them equal:



Cross-multiply





 hours

Edwin
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