Q. 27 PT - Algebra 1

Question

MULTIPLE CHOICE Lee can shovel the driveway in 3 hours, and Susan can shovel the driveway in 2 hours. How long will it take them working together?

$$\begin{gathered} \mathbf{\text{F }}\mathbf{6}\mathbf{ }\mathbf{hours} \\ \mathbf{G}\mathbf{ }\mathbf{5}\mathbf{ }\mathbf{hours} \\ \mathbf{H}\mathbf{ }\frac{\mathbf{3}}{\mathbf{5}}\mathbf{ }\mathbf{hours} \\ \mathbf{J}\mathbf{ }\frac{\mathbf{6}}{\mathbf{5}}\mathbf{ }\mathbf{hours} \end{gathered}$$

Step-by-Step Solution

Answer

It will take $\frac{6}{5}$ hours for Lee and Susan to shovel the driveway together.

Step 1. Write.

Write the given equation in terms of equation.

Let $x$ be the number of hours Lee and Susan can shovel the driveway together, such that,

$\frac{1}{3}+\frac{1}{2}=\frac{1}{x}$

Step 2. Multiplication.

Multiply numerator and denominator of $\frac{1}{3}$ by 2 and multiply numerator and denominator of $\frac{1}{2}$ by 3.

$\frac{1\cdot 2}{3\cdot 2}+\frac{1\cdot 3}{2\cdot 3}=\frac{1}{x}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{array}{c}\frac{1}{x}=\frac{2}{6}+\frac{3}{6}\\ =\frac{2+3}{6}\\ =\frac{5}{6}\\ x=\frac{6}{5}\end{array}$

Therefore, it will take $\frac{6}{5}$ hours for Lee and Susan to shovel the driveway together.

Option J is the required answer.