Question 1103607
>>>A man can do a certain task in 21 hours,
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So the man's rate in jobs per hour is

1 job per 21 hours or

{{{matrix(1,2,1,job)/matrix(1,2,21,hours)}}},

so his rate in jobs/hour is 

{{{matrix(1,2,1/21,jobs/hour)}}}
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>>>another man can do the task in 28 hours,
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So the other man's rate in jobs per hour is

1 job per 28 hours or

{{{matrix(1,2,1,job)/matrix(1,2,28,hours)}}},

so his rate in jobs/hour is 

{{{matrix(1,2,1/28,jobs/hour)}}}
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>>>a boy can do the task in 48 hours
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That's 1 job per 48 hours or

{{{matrix(1,2,1,job)/matrix(1,2,48,hours)}}},

so his rate in jobs/hour is 

{{{matrix(1,2,1/48,jobs/hour)}}}
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>>>Find how long it will take to do the task if all three work.
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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

{{{matrix(1,2,1,job)/matrix(1,2,x,hours)}}},

so their combined rate in jobs/hour is 

{{{matrix(1,2,1/x,jobs/hour)}}}

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

Their combined rate = {{{1/21+1/28+1/48}}}{{{""=""}}}{{{5/48}}}

So we set them equal:

{{{matrix(1,3,1/x,""="",5/48)}}}

Cross-multiply

{{{matrix(1,3,5x,""="",48)}}}

{{{matrix(1,3,x,""="",48/5)}}}

{{{matrix(1,3,x,""="",9&3/48)}}} hours

Edwin</pre>