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Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?
1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

Respuesta :

Giangiglia

Answer:

1) [tex]\Delta t=-0.5*t_{X}[/tex]

2) [tex]\Delta t=2*t_{X}[/tex]

Step-by-step explanation:

1) X=production rate of X (units/hour)

Y=production rate of Y (units/hour)

C=order (units)

t=working time (hour)

[tex](X+Y)*t_{toghether}=C[/tex]

[tex]X*t_{X}=C[/tex]

[tex]t_{toghether}=2/3*t_{X}[/tex]

Combining:

[tex](X+Y)*2/3*t_{X}=X*t_{X}[/tex]

[tex](X+Y)*2/3=X[/tex]

[tex]Y*2/3=X-2/3*X[/tex]

[tex]Y=2X[/tex]

In time: [tex]t_{Y}=0.5*t_{X}[/tex]

Difference of time: [tex]\Delta t=0.5*t_{X}-t_{X}=-0.5*t_{X}[/tex]

2) [tex]Y*t_{Y}=C[/tex]

[tex]X*t_{X}=C[/tex]

[tex]t_{Y}=2*t_{X}[/tex]

Difference of time: [tex]\Delta t=2*t_{X}-0.5*t_{X}=2*t_{X}[/tex]

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