Convert time to seconds

First, convert the initial time of 4 minutes 10 seconds completely into seconds. Since $1\text{ min} = 60\text{ seconds}$, $4\text{ min} = 240\text{ seconds}$. Adding 10 seconds gives $250\text{ seconds}$.

$t_1 = 4 \times 60 + 10 = 250\text{ s}$

Calculate speed or rate per km

The time taken to cover $2.5\text{ km}$ is $250\text{ seconds}$. Therefore, the time taken to cover $1\text{ km}$ is $\frac{250}{2.5} = 100\text{ seconds}$.

$t_{\text{per km}} = \frac{250}{2.5} = 100\text{ s/km}$

Calculate time for 6 km

Multiply the time taken per kilometer by the target distance of $6\text{ km}$.

$t_2 = 6 \times 100 = 600\text{ seconds}$

Convert seconds back to minutes

Convert $600\text{ seconds}$ into minutes by dividing by $60$.

$t_2 = \frac{600}{60} = 10\text{ minutes}$