To determine Johan's rate of speed in miles per hour, we can use the distance formula \( d = rt \), where:
- \( d \) is the distance traveled,
- \( r \) is the rate of speed (in miles per hour),
- \( t \) is the length of time traveled (in hours).
In Johan's case, we know:
- \( d = 35 \) miles (the distance traveled),
- \( t = 1.75 \) hours (the time it took to travel that distance).
We need to solve for \( r \) (the rate of speed). We can rearrange the formula to solve for \( r \):
\[ r = \frac{d}{t} \]
Now we can plug in the values for \( d \) and \( t \):
\[ r = \frac{35 \text{ miles}}{1.75 \text{ hours}} \]
Performing the division:
- To calculate \( r \):
\[ r = \frac{35}{1.75} \]
To make the division simpler, we can multiply both the numerator and the denominator by 100 to eliminate the decimal:
\[ r = \frac{35 \times 100}{1.75 \times 100} = \frac{3500}{175} \]
Now, dividing \( 3500 \) by \( 175 \):
\[ r = 20 \]
Thus, Johan's rate of speed is 20 miles per hour.
Explanation of the solution:
In this problem, we utilized the distance formula to determine speed. By rearranging the formula to isolate \( r \) and substituting the known values of distance and time, we found that Johan traveled at a rate of 20 miles per hour. This means that, on average, for every hour that Johan rode his bicycle, he covered 20 miles. Understanding how to rearrange the formula is crucial for solving similar real-world problems regarding travel distances, speeds, and times.