Question

if you walk \\(\frac{2}{3}\\) mile and then jog \\(\frac{4}{7}\\) mile, what is the total distance covered? how much farther did you walk than jog?
the total distance covered is \\(\square\\) miles.
(simplify your answer. type an integer, simplified fraction, or mixed number.)

Explanation:

Step1: Find a common denominator

To add $\frac{2}{3}$ and $\frac{4}{7}$, the common denominator of 3 and 7 is $3\times7 = 21$.
Rewrite the fractions: $\frac{2}{3}=\frac{2\times7}{3\times7}=\frac{14}{21}$ and $\frac{4}{7}=\frac{4\times3}{7\times3}=\frac{12}{21}$.

Step2: Add the fractions

Add the numerators: $\frac{14}{21}+\frac{12}{21}=\frac{14 + 12}{21}=\frac{26}{21}$.
Convert to a mixed number: $\frac{26}{21}=1\frac{5}{21}$. But wait, maybe I made a mistake. Wait, no, let's check again. Wait, the problem says "walk $\frac{2}{3}$ mile and then jog $\frac{4}{7}$ mile". Wait, no, maybe the jog is $\frac{4}{7}$? Wait, no, let's recalculate. Wait, $\frac{2}{3}+\frac{4}{7}$. The common denominator is 21. $\frac{2}{3}=\frac{14}{21}$, $\frac{4}{7}=\frac{12}{21}$. So $14 + 12 = 26$, so $\frac{26}{21}$, which is $1\frac{5}{21}$. But maybe the question is about total distance. Wait, but let's check the problem again. Wait, the user's problem: "If you walk $\frac{2}{3}$ mile and then jog $\frac{4}{7}$ mile, what is the total distance covered? How much farther did you walk than jog?" Wait, but the first part is total distance. So total distance is $\frac{2}{3}+\frac{4}{7}$. Let's compute that. $\frac{2}{3}+\frac{4}{7}=\frac{14 + 12}{21}=\frac{26}{21}=1\frac{5}{21}$. But maybe I misread the fractions. Wait, the image shows "walk $\frac{2}{3}$" and "jog $\frac{4}{7}$"? Wait, no, maybe the jog is $\frac{4}{7}$? Wait, no, let's check the arithmetic again. $\frac{2}{3}+\frac{4}{7}$. The least common multiple of 3 and 7 is 21. So $\frac{2\times7}{3\times7}+\frac{4\times3}{7\times3}=\frac{14}{21}+\frac{12}{21}=\frac{26}{21}$. So the total distance is $\frac{26}{21}$ miles or $1\frac{5}{21}$ miles. But maybe the problem has a typo, but assuming the fractions are $\frac{2}{3}$ and $\frac{4}{7}$, that's the calculation.

Wait, but maybe I made a mistake. Wait, let's check again. $\frac{2}{3}$ is approximately 0.666, $\frac{4}{7}$ is approximately 0.571. Adding them gives approximately 1.238, which is $\frac{26}{21}\approx1.238$. So that's correct.

Answer:

The total distance covered is $\boxed{1\frac{5}{21}}$ miles (or $\frac{26}{21}$ miles).