Question

Justin bikes for 2/3 of an hour and jogs for 1/4 of an hour. Then he swims for 1/2 of an hour. How much time does Justin spend biking and jogging before he goes swimming?

Answer 1

To find the total time that Justin spends biking and jogging, we need to add the time he spends biking and the time he spends jogging.

1. **Time spent biking**: \( \frac{2}{3} \) hour
2. **Time spent jogging**: \( \frac{1}{4} \) hour

Next, we need a common denominator to add these fractions together. The denominators are 3 and 4. The least common multiple of 3 and 4 is 12.

Now we convert each fraction to have a denominator of 12:

- For biking:
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]

- For jogging:
\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\]

Now we can add these two fractions together:

\[
\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}
\]

Thus, the total time Justin spends biking and jogging is \( \frac{11}{12} \) of an hour.

To summarize, Justin spends **\( \frac{11}{12} \) of an hour** biking and jogging before he goes swimming.