Question

Patrolman Peterson drove 3½ miles to the police station. Then he drove 4 3/4miles to his first assignment. Next, he drove 3 2/3miles to the courthouse for a meeting. Finally, he drove 3 1/2miles home. How many miles did Patrolman Peterson drive?

Answer 1

To find the total distance that Patrolman Peterson drove, we need to add the distances of each segment of his trip.

1. First distance: \( 3 \frac{1}{2} \) miles
2. Second distance: \( 4 \frac{3}{4} \) miles
3. Third distance: \( 3 \frac{2}{3} \) miles
4. Fourth distance: \( 3 \frac{1}{2} \) miles

Let's convert each mixed number to an improper fraction.

1. \( 3 \frac{1}{2} = \frac{7}{2} \)
2. \( 4 \frac{3}{4} = \frac{19}{4} \)
3. \( 3 \frac{2}{3} = \frac{11}{3} \)
4. \( 3 \frac{1}{2} = \frac{7}{2} \)

Now, we need to find a common denominator to add these fractions. The denominators are 2, 4, and 3. The least common multiple of these numbers is 12.

Now, we convert each fraction:

1. \( \frac{7}{2} = \frac{7 \cdot 6}{2 \cdot 6} = \frac{42}{12} \)
2. \( \frac{19}{4} = \frac{19 \cdot 3}{4 \cdot 3} = \frac{57}{12} \)
3. \( \frac{11}{3} = \frac{11 \cdot 4}{3 \cdot 4} = \frac{44}{12} \)
4. \( \frac{7}{2} = \frac{42}{12} \)

Now, we can add these fractions together:

\[
\frac{42}{12} + \frac{57}{12} + \frac{44}{12} + \frac{42}{12} = \frac{42 + 57 + 44 + 42}{12} = \frac{185}{12}
\]

Next, we convert the improper fraction back to a mixed number:

\[
\frac{185}{12} = 15 \frac{5}{12}
\]

Thus, Patrolman Peterson drove a total distance of \( 15 \frac{5}{12} \) miles.