Working together, two secretaries can stuff the envelopes for a political fund-raising letter in 3 hours. Working alone, it takes the slower worker 8 hours longer to do the job than the faster worker. How long does it take each to do the job alone?

Accepted Solution

Answer:Faster worker takes 4 hours and slower worker takes 12 hours.Step-by-step explanation:Let x be the time ( in hours ) taken by faster worker,So, according to the question,Time taken by slower worker = (x+8) hours,Thus, the one day work of faster worker = [tex]\frac{1}{x}[/tex]Also, the one day work of slower worker = [tex]\frac{1}{x+8}[/tex]So, the total one day work when they work together = [tex]\frac{1}{x}+\frac{1}{x+8}[/tex]Given,They take 3 hours in working together,So, their combined one day work = [tex]\frac{1}{3}[/tex][tex]\implies \frac{1}{x}+\frac{1}{x+8}=\frac{1}{3}[/tex][tex]\frac{x+8+x}{x^2+8x}=\frac{1}{3}[/tex]  ( Adding fractions )[tex]3(2x+8)=x^2+8x[/tex]    ( Cross multiplication )[tex]6x+24=x^2+8x[/tex]       ( Distributive property )[tex]x^2+2x-24=0[/tex]          ( Subtraction property of equality )By quadratic formula,[tex]x=\frac{-2\pm \sqrt{100}}{2}[/tex][tex]x=\frac{-2\pm 10}{2}[/tex][tex]\implies x=4\text{ or }x=-6[/tex]Since, hours can not negative,Hence, time taken by faster worker = x hours = 4 hours,And, the time taken by slower worker = x + 8 = 12 hours.