Question

A factory has two bottle filling machines, which run at the same time. Machine B fills bottles at a rate of x, which is 1.5 times the rate of Machine A. The factory is considering buying a new machine that would replace the other two machines. It can fill at a rate of 3x.
If the factory buys the new machine to replace the other two, which of the following expressions show the increase in rate?

Answer 1

Answer:

$\dfrac{4}{3}x$

Step-by-step explanation:

Given that:

Rate of bottle filling for Machine B = $x$

Rate of filling of Machine B is 1.5 times the rate of Machine A.

Let the rate of bottle filling for Machine A = $y$

As per question statement:

$x=1.5y\\\Rightarrow y=\dfrac{2}{3}x$

Now, combined rate of both the machines, i.e. A and B = $x+y$

$\Rightarrow x+\dfrac{2}{3}x\\\Rightarrow \dfrac{5}{3}x$

Bottle filling Rate of new Machine = $3x$

It is given that both the machines are replaced by the new machine.

Now, increase in the rate can be calculated by subtracting the combined rate of both the machines from the bottle filling rate of new machine.

i.e.

$3x-\dfrac{5x}3\\\Rightarrow \dfrac{9x-5x}{3}\\\Rightarrow \bold{\dfrac{4x}{3}}$

So, the following expression shows the increase in rate:

$\dfrac{4}{3}x$