Question

Jay and Kevin are shoveling the snow off a driveway. Working together, they can clear the driveway of snow in 14 minutes. Working alone, itwould 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 wouldtake Jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation:How long would it take jay to clear the driveway of snow working alone?

Answer 1

The Solution:

The correct answer is j = 21 [option B]

Given:

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

We are required to solve for j.

$\begin{gathered} \frac{1}{j}+\frac{1}{j+21}=\frac{1}{14} \\ \\ \frac{j+21+j}{j(j+21)}=\frac{1}{14} \end{gathered}$$\frac{2j+21}{j(j+21)}=\frac{1}{14}$

Cross multiply:

$\begin{gathered} j(j+21)=14(2j+21) \\ j^2+21j=28j+294 \\ j^2+21j-28j-294=0 \end{gathered}$$undefined$