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 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.
Johan travels at a rate of 61.25 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 10 miles per hour.

Answer 1

To find Johan's rate of speed (r), we can use the distance formula \( d = rt \). We have the distance (d) traveled and the time (t) it took, and we need to find the rate (r).

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

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

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

Now we can substitute the values into the equation:

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

Calculating this:

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

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

Explanation of the Solution

In this real-world problem, we first identified the known quantity (distance traveled) and the time taken to travel that distance. By rearranging the formula for distance, we could isolate the variable we were interested in, which was the rate of speed. Performing the division of distance by time provided the answer that represents Johan's average speed during his bicycle ride.