Question

select the correct answer.

jay and kevin are shoveling the snow off a driveway. working together, they can clear the driveway of snow in 14 minutes. working alone, it would take kevin 21 minutes longer to clear the driveway of snow than it would take jay working alone. when \\(j\\) is the number of minutes it would take jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation:

\\\frac{1}{j} + \frac{1}{j + 21} = \frac{1}{14}\\

how long would it take jay to clear the driveway of snow working alone?

• 7 minutes
• 21 minutes
• 35 minutes
• 42 minutes

Explanation:

Set up the rational equation

$$ \frac{1}{j} + \frac{1}{j + 21} = \frac{1}{14} $$

Clear the denominators by multiplying by \(14j(j + 21)\)

$$ 14(j + 21) + 14j = j(j + 21) $$

$$ 14j + 294 + 14j = j^2 + 21j $$

$$ 28j + 294 = j^2 + 21j $$

Solve the quadratic equation for \(j\)

$$ j^2 - 7j - 294 = 0 $$

$$ (j - 21)(j + 14) = 0 $$

$$ j = 21 \quad \text{or} \quad j = -14 $$

Since time must be positive, \(j = 21\).

Answer:

• 7 minutes
• 21 minutes (Correct answer)
• 35 minutes
• 42 minutes