Question

Tracy can lay a slab of concrete in 3 hours, with Jordan’s help they can do it in 2 hours. If Jordan works alone, how long will it take?

Short answer

If Jordan works alone then he will take 6 hours.

Step-by-step solution

Given information

The problem has the information of the work done by Tracy and Jordan.

Form the rational equation and solve

Use the given sentence to form the required rational equation.

• As given, Tracy(T) takes 3 hours to work alone whereas Tracy (T) and Jordan(J) together take 2 hours.
• Hence the equation is formed as $\frac{1}{3}+\frac{1}{J}=\frac{1}{2}.............\left(1\right)$.
• Now solve equation (1) to find the time taken by Jordan(J) alone.

$\begin{array}{rcl}\frac{1}{3}+\frac{1}{J}& =& \frac{1}{2}\\ \frac{1}{J}& =& \frac{1}{2}-\frac{1}{3}\\ & =& \frac{3-2}{6}\\ & =& \frac{1}{6}\\ J& =& 6\end{array}$