Brian ran a 5-kilometer race in 40 minutes. How far did he run in 18 minutes? Write your answer as a decimal and do not round.
The problem involves calculating distance covered under the condition of constant speed. We know that Brian completed a 5-kilometer race in 40 minutes. Because his speed remained constant, we can establish his rate of speed by dividing the total distance by the total time taken. The objective is to determine how far he ran in exactly 18 minutes by multiplying this constant speed by the new time duration.
To find Brian's speed in kilometers per minute, we use the formula for speed:
\[v = \frac{\text{distance}}{\text{time}} = \frac{5 \text{ km}}{40 \text{ min}}\]
Calculating this division, we find:
\[v = \frac{5}{40} = 0.125 \text{ km/min}\]
This means Brian covers 0.125 kilometers for every minute of running.
Now that we have the constant speed, we calculate the distance covered in 18 minutes using the formula \(\text{distance} = \text{speed} \times \text{time}\):
\[d = 0.125 \text{ km/min} \times 18 \text{ min}\]
Multiplying these values, we get:
\[d = 2.25 \text{ km}\]
Thus, in 18 minutes, Brian ran exactly 2.25 kilometers.
Understanding how to calculate distance from constant speed is essential for travel planning and time management. For instance, if you know the average speed of a train or a bus, you can calculate exactly when it will reach a certain landmark or how far it will travel in a given amount of time. This fundamental skill helps in scheduling daily commutes and understanding movement in everyday life.