Question

It would take Charlene and Gina 18 minutes to organize Charlene’s comic book collection if they work together. If Gina works alone, it would take her 15 minutes longer than it would take Charlene working alone. When x represents the number of minutes it takes Charlene to organize the comic book collection working alone, the situation is represented by this equation: \frac{1}{x} \ + \ \frac{1}{x\:+\:15} \ = \ \frac{1}{18}. Which value is a solution of the rational equation that must be discarded because of the context?

Answer 1

Answer【Answer】：B

【Explanation】： The question is about investigating the possible exchange rate for that discussion. If Charlene can prepare her book collection in x minutes when working alone and Gina needs another 15 minutes, then the reason is that Gina cannot prepare her collection in x+15 minutes. Therefore, the situation can be expressed by the equation, which is 1/x for Charlene and the number of colors is 1/(x + 15) for Gina.

The values given are x = 0, x = -9, x = -15, and x = -30.

The scope is important to ensure proper functioning. If x represents the period required for Charlene to delete the archive, then it must not become decreasing. The same as minutes, large or equal to a whole number. x represents an unreduced quantity. If x = -9, that is, time , it is impossible. So, option B is the correct discriminative solution in the original question, with x = -9 not sounding sensible given the situation. However, it is the correct answer.

Answer 2

Therefore, the correct answer is: B. x = -9

To solve the rational equation
`\( (1)/(x) + (1)/(x+15) = (1)/(18) \)` and identify the value that must be discarded due to the context, let's follow these steps:

1. Find a common denominator for the fractions on the left side of the equation, which is
`\(18x(x+15)\)`:

`\[ (18(x+15) + 18x)/(18x(x+15)) = (1)/(18) \]`

2. Combine the numerators on the left side:

`\[ (36x + 270 + 18x)/(18x(x+15)) = (1)/(18) \]`

`\[ (54x + 270)/(18x(x+15)) = (1)/(18) \]`

3. Simplify the equation:

`\[ (3x + 15)/(x(x+15)) = (1)/(18) \]`

4. Cross-multiply to get rid of the fractions:

`\[ 18(3x + 15) = x(x+15) \]`

`\[ 54x + 270 = x^2 + 15x \]`

5. Move all terms to one side of the equation:

`\[ x^2 - 39x - 270 = 0 \]`

6. Factor the quadratic equation:

`\[ (x - 30)(x + 9) = 0 \]`

This gives two possible solutions:
`\( x = 30 \) and \( x = -9 \)`.

Now, let's consider the context of the problem. The time it takes cannot be negative, so we discard the solution x = -9 .

Complete the question:

Select the correct answer. It would take Charlene and Gina 18 minutes to organize Charlene's comic book collection if they work together. If Gina works alone, it would take her 15 minutes longer than it would take Charlene working alone. When x represents the number of minutes it takes Charlene to organize the comic book collection working alone, the situation is represented by this equation: 1/x + 1/x+15 = 1/18 . Which value is a solution of the rational equation that must be discarded because of the context? A. x=0 B. x=-9 C. x=-15 D. x=-30