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.
