To determine Johan's rate of speed, we can use the distance formula \( d = rt \), where:
- \( d \) is the distance traveled (in miles),
- \( r \) is the rate of speed (in miles per hour),
- \( t \) is the length of time traveled (in hours).
We know the following values from the problem:
- \( d = 35 \) miles
- \( t = 1.75 \) hours
We need to solve for \( r \). Rearranging the distance formula gives us:
\[
r = \frac{d}{t}.
\]
Substituting the known values into this equation:
\[
r = \frac{35 \text{ miles}}{1.75 \text{ hours}}.
\]
Now, we can perform the calculation:
\[
r = 35 \div 1.75.
\]
To simplify this division, it may help to convert \( 1.75 \) into a fraction. We know that \( 1.75 = \frac{7}{4} \). Thus we can rewrite the expression as:
\[
r = 35 \div \frac{7}{4} = 35 \times \frac{4}{7} = \frac{35 \times 4}{7}.
\]
Calculating \( \frac{35 \times 4}{7} \):
\[
35 \div 7 = 5.
\]
Then,
\[
5 \times 4 = 20.
\]
So, \( r = 20 \) miles per hour.
Thus, Johan travels at a rate of
\[
\boxed{20} \text{ miles per hour} \quad (Option B).
\]
**Explanation of Solution:**
Johan's rate of speed is calculated by taking the total distance traveled (35 miles) and dividing it by the time taken to travel that distance (1.75 hours). This gives us the average speed in miles per hour. In practical terms, knowing the speed helps Johan (or anyone else) understand how fast they are biking and make plans accordingly, such as how long it will take to reach a destination.