Question

Derek rode his bike for 2 5/8 miles on Wednesday. On Thursday, he biked 5 1/3 times as far as on Wednesday. How many miles did Derek bike on Thursday?

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

Answer 1

To find out how many miles Derek biked on Thursday, we first need to convert the mixed numbers into improper fractions.

1. **Convert 2 5/8 to an improper fraction:**
\[
2 \frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}
\]

2. **Convert 5 1/3 to an improper fraction:**
\[
5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
\]

3. **Now, calculate the distance Derek biked on Thursday by multiplying the distance he biked on Wednesday by 5 1/3:**
\[
\text{Distance on Thursday} = \frac{21}{8} \times \frac{16}{3}
\]

4. **Multiply the fractions:**
\[
= \frac{21 \times 16}{8 \times 3} = \frac{336}{24}
\]

5. **Simplify \(\frac{336}{24}\):**
To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 24.
\[
\frac{336 \div 24}{24 \div 24} = \frac{14}{1} = 14
\]

Thus, Derek biked **14 miles** on Thursday.