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At Pizza Perfect, Ron and Harold make pizza crusts. When they work separately Ron finishes the job of making 100 crusts 1.2 hours before Harold finishes the same job. When they work together they finish making 100 crusts in 1.8 hours. How many hours, to the nearest tenth of an hour, does it take Ron working alone to make 100 crusts?

Respuesta :

Answer:  Ron take approximately 4.2 hours to make 100 crusts alone.

Step-by-step explanation:

Since we have given that

Number of hours taken by Ron before Harold = 1.2 hours

Number of hours taken by Ron and Harold together = 1.8 hours

We need to find the number of hours taken by Ron alone i.e. 'x'.

Let number of hours taken by Harold alone be '1.2-x'.

Let work done by Ron alone  = [tex]\dfrac{1}{x}[/tex]

Work done by Harold = [tex]\dfrac{1}{x-1.2}[/tex]

According to question, we get that

[tex]\dfrac{1}{x}+\dfrac{1}{x-1.2}=\dfrac{1}{1.8}\\\\\dfrac{x-1.2+x}{x(x-1.2)}=\dfrac{1}{1.8}\\\\\dfrac{2x-1.2}{x^2-1.2x}=\dfrac{1}{1.8}\\\\3.6x-2.16=x^2-1.2x\\\\x^2-1.2x-3.6x+2.16=0\\\\x^2-4.8x+2.16=0\\\\x=0.5,4.2[/tex]

x-1.2 does not satisfied with x = 0.5 so, x = 4.2

Hence, Ron take approximately 4.2 hours to make 100 crusts alone.