The distance formula can be written as d=rt

Question

, 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.(1 point)
Responses

Johan travels at a rate of 10 miles per hour.
Johan travels at a rate of 10 miles per hour.

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

Johan travels at a rate of 2 miles per hour.
Johan travels at a rate of 2 miles per hour.

Johan travels at a rate of 61.25 miles per hour.

Answer 1

To find Johan's rate of speed in miles per hour using the distance formula \( d = rt \), we can rearrange the formula to solve for the rate \( r \):

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

In this problem, we know:

• \( d = 35 \) miles (distance traveled)
• \( t = 1.75 \) hours (time traveled)

Now, we can plug in the values:

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

Calculating this gives:

\[ r = 20 \text{ miles per hour} \]

Thus, Johan travels at a rate of 20 miles per hour.

Explanation of the solution:

To calculate Johan's speed, we used the distance formula which relates distance, speed, and time. By isolating the rate in the equation, we could directly compute it using the known distance and time values. In this case, after performing the division of 35 miles by 1.75 hours, we found that Johan travels at a speed of 20 miles per hour.