To find Johan's rate of speed, we'll use the distance formula d = rt, where:
- \( d \) is the distance traveled,
- \( r \) is the rate of speed (which we want to find),
- \( t \) is the time traveled.
Johan's distance traveled \( d \) is 35 miles, and the time traveled \( t \) is 1.75 hours. We can rearrange the formula to solve for the rate \( r \):
\[ r = \frac{d}{t} \]
Now we can substitute in the known values:
\[ r = \frac{35 \text{ miles}}{1.75 \text{ hours}} \]
To perform the division, we can calculate:
\[ r = 35 \div 1.75 \]
Now, converting 1.75 into a fraction for easier calculation:
1.75 = 175 / 100 = 7 / 4
Now, we can rewrite the division:
\[ r = 35 \div (7/4) = 35 \times \frac{4}{7} \]
Multiplying:
\[ r = 35 \times \frac{4}{7} = 20 \text{ miles per hour} \]
Therefore, Johan’s rate of speed is 20 miles per hour.
Explanation:
In this real-world problem, we assessed Johan's biking speed by understanding how distance, time, and speed relate. By extracting the necessary values (distance traveled and time taken) and applying them to the distance formula, we calculated his speed. This calculation allows us to understand how efficiently Johan is traveling, which can be applied to various contexts, such as planning trips or assessing fitness levels.