Sandeep mailed a letter on Monday morning. The letter traveled 10 1/6 miles on Monday. It traveled 5 more miles on Tuesday, reaching its destination on Tuesday afternoon. How far did Sandeep's letter travel in all?

Question

Write your answer as a fraction or as a whole or mixed number

Answer 1

To find the total distance that Sandeep's letter traveled, we need to add the distance it traveled on Monday and the distance it traveled on Tuesday.

On Monday, the letter traveled \(10 \frac{1}{6}\) miles.

On Tuesday, it traveled 5 miles.

First, we convert \(10 \frac{1}{6}\) into an improper fraction: \[ 10 \frac{1}{6} = 10 + \frac{1}{6} = \frac{60}{6} + \frac{1}{6} = \frac{61}{6} \]

Next, we express the distance traveled on Tuesday as a fraction. Since 5 can be expressed as \( \frac{5}{1} \), we convert it to a fraction with a common denominator of 6: \[ 5 = \frac{5 \times 6}{1 \times 6} = \frac{30}{6} \]

Now we can add the distances traveled on both days: \[ \frac{61}{6} + \frac{30}{6} = \frac{61 + 30}{6} = \frac{91}{6} \]

To present \(\frac{91}{6}\) as a mixed number, we perform the division: \[ 91 \div 6 = 15 \quad \text{(with a remainder of 1)} \] Thus, \(\frac{91}{6} = 15 \frac{1}{6}\).

Therefore, the total distance that Sandeep's letter traveled is: \[ \boxed{15 \frac{1}{6}} \text{ miles} \]