To determine the distance traveled in this problem, we need to follow a systematic approach. Let's break down the steps:
1. Identify the given values:
- The speed of the point, [tex]\( v \)[/tex], is given as [tex]\( 2.4 \)[/tex] miles per hour.
- The time, [tex]\( t \)[/tex], is given as [tex]\( 15 \)[/tex] minutes.
2. Convert time from minutes to hours:
Since speed is given in miles per hour, we should convert the time into hours to be consistent with the units of speed. There are 60 minutes in an hour, so:
[tex]\[
\text{time in hours} = \frac{\text{time in minutes}}{60}
\][/tex]
Substituting the given time:
[tex]\[
\text{time in hours} = \frac{15}{60} = 0.25 \text{ hours}
\][/tex]
3. Calculate the distance traveled:
The distance, [tex]\( s \)[/tex], travelled is determined using the formula:
[tex]\[
\text{distance} = \text{speed} \times \text{time}
\][/tex]
Substituting the values for speed and time:
[tex]\[
s = 2.4 \text{ miles per hour} \times 0.25 \text{ hours}
\][/tex]
Performing the multiplication:
[tex]\[
s = 0.6 \text{ miles}
\][/tex]
Therefore, the exact distance travelled is:
[tex]\[
s = 0.6 \text{ miles}
\][/tex]
