Respuesta :
Answer:
Machine A take 6 hours to produce 1 widget on its own.
Step-by-step explanation:
Consider the provided information.
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates.
Let Machine A takes 'x' hours to produce 1 widget.
Thus, in every hour it will produce [tex]\frac{1}{x}[/tex] th of widget.
Similarly Machine B takes 'y' hours to produce 1 widget.
In every hour it will produce [tex]\frac{1}{y}[/tex] th of widget.
If both machine work together they can produce 1 widget in 3 hrs.
Therefore, work done by A and B together in 1 hour is:
[tex]\frac{1}{3} =\frac{1}{x}+\frac{1}{y}[/tex] ......(1)
If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates.
[tex]\frac{1}{2} =\frac{2}{x}+\frac{1}{y}[/tex] ......(2)
Subtract equation 1 from equation 2.
[tex]\frac{1}{2}-\frac{1}{3}=\frac{2}{x}-\frac{1}{x}+\frac{1}{y}-\frac{1}{y}[/tex]
[tex]\frac{3-2}{6}=\frac{2-1}{x}[/tex]
[tex]\frac{1}{6}=\frac{1}{x}[/tex]
[tex]x=6[/tex]
Hence, machine A take 6 hours to produce 1 widget on its own.
