Question

Running at their respective constant rates. Machine A takes 4 days longer to produce widgets than Machine B. At these rates, if the two machines work together to produce 2x widgets in 3 days, how many days would it take Machine A alone to produce $\frac{5}{2}$ x widgets?

Answer 1

Days required to produce $x$ widgets by B $\to D$

Days required to produce $\frac{x}{D}$ widgets by B $\to 1Day$

Days required to produce $x$ widgets by A $\to D+4$

Days required to produce $\frac{x}{D+4}$ widgets by A $\to 1Day$

Days required to produce $2x$ widgets when both work together $\to 3Day$

Days required to produce $\frac{2x}{3}$ widgets when both work together $\to 1Day$

So, $\frac{x}{D+4}+\frac{x}{D}=\frac{2x}{3}\Rightarrow 2D^2+2D-12=0\Rightarrow D^2+D-6=0\Rightarrow D=2$

Hence Days required to produce $x$ widgets by A $\to 2+4$

Hence Days required to produce $x$ widgets by A $\to 6$

Hence Days required to produce $\frac{5}{2}x$ widgets by A $\to \frac{5}{2}\times 6=15Day$