Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a p

Question

2 months ago

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Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a p

roduction 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 ?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-04T14:35:31+03:00

Answer:

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

Step-by-step explanation:

Machine A = 5 hours

Machine B = x hours

When both machines work together, it takes 2 hours.

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

where:

T represents the total time worked by both machines

A represents the time taken by Machine A

B represents the time taken by Machine B

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

Multiplying all terms by the common denominator (5B),

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

2x + 10 = 5x.

Combining like terms yields:

10 = 5x - 2x

10 = 3x;

To isolate x, divide both sides by 3.

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

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

Thus, Machine B will require $\frac{10}{3}$ hours to fill the lot.