The distance formula can be written as d = rt, where d = distance traveled, r = the rate of speed, and t = the length of time traveled. Johan travels 35 miles by bicycle in 1.75 hours. What is Johan's rate of speed in miles per hour? Explain the solution to the real-world problem.

Question

A. Johan travels at a rate of 2 miles per hour.
B. Johan travels at a rate of 20 miles per hour.
C. Johan travels at a rate of 10 miles per hour.
D. Johan travels at a rate of 61.25 miles per hour.

Answer 1

To find Johan's rate of speed, we can use the formula \(d = rt\). Here, \(d\) is the distance traveled, \(r\) is the rate of speed (in miles per hour), and \(t\) is the time traveled (in hours).

We are given:

• Distance traveled, \(d = 35\) miles
• Time traveled, \(t = 1.75\) hours

We can rearrange the formula to solve for the rate of speed \(r\):

\[ r = \frac{d}{t} \]

Now we can substitute in the values we have:

\[ r = \frac{35 , \text{miles}}{1.75 , \text{hours}} \]

To perform the division:

1. First, convert \(1.75\) into a fraction: \(1.75 = \frac{7}{4}\).
2. This gives us:

\[ r = \frac{35}{1.75} = \frac{35 \times 4}{7} = \frac{140}{7} = 20 \text{ miles per hour} \]

Thus, Johan's rate of speed is 20 miles per hour.

So, the correct answer is:

B. Johan travels at a rate of 20 miles per hour.

Explanation:

This rate of speed indicates how fast Johan is biking; he covers 20 miles in one hour. By using the distance formula \(d = rt\) and rearranging it to solve for \(r\), we accurately calculated the speed based on the distance he traveled and the time taken. This approach systematically applied the formula to derive the required information from the real-world context.