Question

A train is traveling at a rate of 3.2 kilometers per minute.

Question
Which equation can be used to find the number of minutes, m, the train travels in k kilometers?

Answer options with 4 options
A.
m equals 0.3125 k

B.
m equals 3.2 k

C.
m equals k plus 0.3125

D.
m equals k plus 3.2

Answer 1

To find the number of minutes \( m \) the train travels in \( k \) kilometers, we need to use the relationship between distance, rate, and time. The formula that relates these three is:

\[
\text{Distance} = \text{Rate} \times \text{Time}
\]

In this case, we have:

- Distance = \( k \) kilometers
- Rate = \( 3.2 \) kilometers per minute
- Time = \( m \) minutes

We can rearrange the formula to solve for \( m \):

\[
m = \frac{\text{Distance}}{\text{Rate}} = \frac{k}{3.2}
\]

Now, to express \( \frac{k}{3.2} \) in a form that allows us to find the proper relationship to select from the answer options, we can rewrite \( \frac{1}{3.2} \):

\[
\frac{1}{3.2} = 0.3125
\]

Thus, the relationship becomes:

\[
m = 0.3125 \times k
\]

So, the correct equation is:

**A. \( m = 0.3125 k \)**