Question

Pam walks $\dfrac{7}{8}$ of a mile to school. Paul walks $\dfrac{1}{2}$ of a mile to school. How much farther does Pam walk than Paul?

Answer 1

Hint: The distance walked by Pam is given to be equal to $\dfrac{7}{8}$ of a mile, while the distance walked by Paul is given to be equal to $\dfrac{1}{2}$. So the difference between the distance walked by Pam and that by Paul will be equal to the distance which Pam walks farther than Paul. So we need to take the difference of $\dfrac{7}{8}$ and $\dfrac{1}{2}$, that is, $\dfrac{7}{8}-\dfrac{1}{2}$. For calculating this difference, we need to take the LCM of the denominators of both the numbers. Then on simplifying, we will get the final answer.

Complete step by step solution:
Let the distance travelled by Pam towards the school be $x$ of a mile and that travelled by Paul be $y$ of a mile.
According to the question, Pam walks $\dfrac{7}{8}$ of a mile while Paul walks $\dfrac{1}{2}$ of a mile to the school. So we have
\[\Rightarrow x=\dfrac{7}{8}\], and
\[\Rightarrow y=\dfrac{1}{2}\]
Now, clearly the distance travelled by Pam is greater than that by Paul. So the distance through which Pam walks farther than Paul is given by
$\Rightarrow d=x-y$
Substituting the first two equations into the above equation, we get
$\Rightarrow d=\dfrac{7}{8}-\dfrac{1}{2}$
Now, for subtracting or adding the two fractions, we need to make the denominators of both the fractions same. For this, we consider the LCM of the denominators of both the fractions, that is, the LCM of $2$ and $8$. Since $8$ is a multiple of $2$, so the LCM of $2$ and $8$ is equal to $8$. So we make the denominator of the second fraction of the above equation equal to $8$ as
$\begin{align}
  & \Rightarrow d=\dfrac{7}{8}-\dfrac{1}{2}\times \dfrac{4}{4} \\
 & \Rightarrow d=\dfrac{7}{8}-\dfrac{4}{8} \\
 & \Rightarrow d=\dfrac{7-4}{8} \\
 & \Rightarrow d=\dfrac{3}{8} \\
\end{align}$
Hence, Pam walks a distance of $\dfrac{3}{8}$ of a mile farther than Paul.

Note: Do not forget to answer the given question in miles, since the distances covered are given in miles. We can also solve this question by converting the given distances in the fractional form to the decimal form. For this we have to carry out the required division. And then, we can easily subtract the two decimal numbers to get the final answer.