Question

Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

Answer 1

$\boldsymbol{\mathbf{Answer}}$

$\boldsymbol{\mathbf{Machine \, A \,will\, take \,6 \,hours\, to \,produce\, 1 \,widget \,on\, its\, own.}}$

$\boldsymbol{\mathbf{Step-by-step \,explanation:}}$

Let,

performance rate of machine A is x widget per hour.

performance rate of machine A is y widget per hour.

As given, Machine A and Machine B can produce 1 widget in 3 hours working together.

I.e mathemetically,

$\boldsymbol{x + y=\frac{1}{3}......(1)}$

lly for second statement, Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together.

i.e mathematically,

$\boldsymbol{2x + y=\frac{1}{2}......(2)}$

Substact equation (1) in (2)

  $x + y=\frac{1}{3}$

$-2x + y=\frac{1}{2}$

Resultant equation will be,

$-x=\frac{-1}{6}$

$\boldsymbol{x = \frac{1}{6}}$

Performance rate of machine A is \frac{1}{6} widget per hour.

what is time Machine A will take to produce 1 widget on its own.

i.e = $\frac{1}{\frac{1}{6}}$

$\boldsymbol\mathbf{{=\, 6 \,hours.}}$