Question

Jerome rides 35/6 miles in an hour with a constant speed. If he rides for 8/7 hours, find the distance that he covers.
20/3 miles
35/3 miles
124/21 miles
-124/21 miles

Answer 1

To find the distance that Jerome covers, we can use the formula for distance, which is:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

In this case, Jerome's speed is \(\frac{35}{6}\) miles per hour, and his riding time is \(\frac{8}{7}\) hours.

1. **Calculate the distance:**

\[
\text{Distance} = \frac{35}{6} \times \frac{8}{7}
\]

2. **Multiply the fractions:**

To multiply the fractions, we multiply the numerators and the denominators:

\[
\text{Distance} = \frac{35 \times 8}{6 \times 7}
\]

Calculating the numerator and denominator:

- Numerator: \(35 \times 8 = 280\)
- Denominator: \(6 \times 7 = 42\)

So we have:

\[
\text{Distance} = \frac{280}{42}
\]

3. **Simplify the fraction:**

We can simplify \(\frac{280}{42}\):

To simplify:

\[
\frac{280}{42} = \frac{280 \div 14}{42 \div 14} = \frac{20}{3}
\]

Thus, the distance that he covers is:

\[
\boxed{\frac{20}{3}} \text{ miles}
\]