Mathematics: Machines a and b always operate independently and at their respective constant rates. when working alone, machine a can fill a production lot in 5 hours, and machine b can fill the same lot in x hours. when the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. what is the value of x ?

Machines a and b always operate independently and

makayladurham19

11.01.2022

The value of x is $\frac{10}{3}$ hours.

Step-by-step explanation:

Machine A = 5 hours

Machine B = x hours

Machine A and B = 2 hours

Using the formula: $\frac{T}{A} + \frac{T}{B} = 1$

where:

T is the time spend by both machine

A is the time spend by machine A

B is the time spend by machine B

$\frac{2}{5} + \frac{2}{x} = 1$

Let multiply the entire problem by the common denominator (5B)

$5x(\frac{2}{5} + \frac{2}{x} = 1)$

2x + 10 = 5x

Collect the like terms

10 = 5x - 2x

10 = 3x

3x = 10

Divide both side by the coefficient of x (3)

$\frac{3x}{3} = \frac{10}{3}$

$x = \frac{10}{3}$ hours.

Therefore, Machine B will fill the same lot in $\frac{10}{3}$ hours.

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Yoma321

20.12.2022

C, a square is equiangular and equilateral.

Equilateral- Having all sides of the same length (the sides of a square are all congruent).

Equiangular- Having all angles of the same measure/degree. A square is made up of four 90° angles.

Hope this helps,

LaciaMelodii :)

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