Question

Solving Linear Equations Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
8 of 158 of 15 Items


















Question
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.(1 point)
Responses

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

Answer 1

To find Johan’s rate of speed, we can use the distance formula, which is given by:

\[ d = rt \]

Where:
- \( d \) is the distance traveled (in miles)
- \( r \) is the rate of speed (in miles per hour)
- \( t \) is the length of time traveled (in hours)

From the problem:
- \( d = 35 \) miles
- \( t = 1.75 \) hours

We need to find \( r \). We can rearrange the formula to solve for \( r \):

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

Now, substituting the values:

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

To perform the division:

1. Convert 1.75 hours to a fraction to make calculations clearer:
\[ 1.75 = \frac{175}{100} = \frac{7}{4} \]

2. Now, we will divide 35 by \( \frac{7}{4} \):
\[
r = 35 \div \frac{7}{4} = 35 \times \frac{4}{7} = \frac{140}{7} = 20
\]

So, Johan's rate of speed is:

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