Question

Braden bike 10 8/9 miles on Monday on Tuesday he back 3/4 as far as Monday how many total miles did he bike over the two days?

Answer 1

To find out how far Braden biked on Tuesday, we first need to determine how far he biked on Monday, which is given as \(10 \frac{8}{9}\) miles.

1. Convert \(10 \frac{8}{9}\) to an improper fraction:
\[
10 \frac{8}{9} = \frac{10 \times 9 + 8}{9} = \frac{90 + 8}{9} = \frac{98}{9}
\]

2. Now calculate how far he biked on Tuesday, which is \( \frac{3}{4} \) of the distance he biked on Monday:
\[
\text{Distance on Tuesday} = \frac{3}{4} \times \frac{98}{9} = \frac{3 \times 98}{4 \times 9} = \frac{294}{36}
\]

3. Simplifying \( \frac{294}{36} \):
\[
\frac{294}{36} = \frac{49}{6} \quad \text{(dividing the numerator and denominator by 6)}
\]

4. Now we convert \( \frac{49}{6} \) to a mixed number:
\[
\frac{49}{6} = 8 \frac{1}{6}
\]

5. Now we can find the total distance Braden biked over the two days:
\[
\text{Total distance} = \frac{98}{9} + \frac{49}{6}
\]

6. To add these fractions, we need a common denominator. The least common multiple of 9 and 6 is 18:
- Convert \( \frac{98}{9} \) to have a denominator of 18:
\[
\frac{98}{9} = \frac{98 \times 2}{9 \times 2} = \frac{196}{18}
\]
- Convert \( \frac{49}{6} \) to have a denominator of 18:
\[
\frac{49}{6} = \frac{49 \times 3}{6 \times 3} = \frac{147}{18}
\]

7. Now add the two fractions:
\[
\frac{196}{18} + \frac{147}{18} = \frac{196 + 147}{18} = \frac{343}{18}
\]

8. Convert \( \frac{343}{18} \) to a mixed number:
\[
\frac{343}{18} = 19 \frac{1}{1} \quad \text{(since } 343 \div 18 = 19 \text{ remainder } 1\text{)}
\]

Thus, the total miles Braden biked over the two days is:
\[
\boxed{19 \frac{1}{18}}
\] miles.