If a group of 5 craftsmen takes 3 hours to finish a job

Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

\(time*speed=distance\) <--> \(time*rate=job \ done\).

So, if we say that the rate of a craftsmen is \(x\) job/hours and the rate of an apprentice is \(y\) job/hour then we'll have \((5x)*3=job=(4y)*t\) --> \((5x)*3=(4y)*t\). Question: \(t=\frac{15x}{4y}=?\)

(1) Each apprentice works at 2/3 the rate of a craftsman --> \(y=\frac{2}{3}x\) --> \(\frac{x}{y}=\frac{3}{2}\) --> \(t=\frac{15x}{4y}=\frac{45}{8}\) hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): \(\frac{5x}{4y}=\frac{15}{8}\) --> \(\frac{x}{y}=\frac{3}{2}\), the same info as above. Sufficient.

Answer: D.

Could you please elaborate on the highlighted part?

we know 5 craftmen take 3 hours to complete 1 work.
we have to find out 5 craftmen will do how much work in 45/23 hours
5 crafts men is common in both statement.
so they do 1 work in 3 hours ( 1 work =3 hours)
and x work in 45/23 hours (x work = 45/23 hours)
cross multiplying,
x = (45/23)/3
x = 15/23
so 5 craftsmen can do 15/23 work in 45/23 hour.
hope its clear.

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