Question 152882
Let x=# of hours apprentice can complete the job



{{{W=RT}}} Start with the work done formula.


Since the "man can construct a wall in 20 hrs", this means that T=20 



{{{1=R(20)}}} Plug in {{{W=1}}} (for 1 job) and {{{T=20}}}



{{{1/20=R}}} Divide both sides by 20.



So the man's rate is {{{1/20}}} of a wall per hour



{{{W=RT}}} Go back to the first formula



{{{1=Rx}}} Plug in {{{W=1}}} and {{{T=x}}}



{{{1/x=R}}} Divide both sides by x.



So the apprentice's rate is {{{1/x}}} of a wall per hour



Now add the two rates to get {{{R=1/20+1/x=x/(20x)+20/(20x)=(x+20)/(20x)}}}



So together, their rate is {{{R=(x+20)/(20x)}}}



{{{W=RT}}} Go back to the first formula



{{{1=((x+20)/(20x))(12)}}} Plug in {{{W=1}}}, {{{R=(x+20)/(20x)}}}, and {{{T=12}}} (this is the time for them if they work together)



{{{20x=12(x+20)}}} Multiply both sides by {{{20x}}}.



{{{20x=12x+240}}} Distribute



{{{20x-12x=240}}} Subtract {{{12x}}} from both sides.



{{{8x=240}}} Combine like terms on the left side.



{{{x=(240)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}.



{{{x=30}}} Reduce.



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Answer:


So the answer is {{{x=30}}} which means that it'll take 30 hours for the apprentice to do it alone.