Gavin goes for a run at a constant pace of 9 minutes per mile. Ten minutes later, Lars goes for a run, along the same route, at a constant pace of 7 minutes per mile. How many minutes does it take for Lars to reach Gavin?

Step-by-step explanation: Given that Gavin goes for a run at a constant pace of 9 minutes per mile and after 10 minutes, Lars started running along the same route, at a constant pace of 7 minutes per mile. We need to find the number of minutes Lars will take to reach Gavin.

In 9 minutes, distance run by Gavin = 1 mile.

So, in 1 minute, distance travelled by Gavin will be

[tex]d_G=\dfrac{1}{9}=\dfrac{7}{63}~\textup{miles}.[/tex]

Similarly,

In 7 minutes, distance run by Lars = 1 mile.

So, in 1 minute, distance travelled by Lars will be

[tex]d_L=\dfrac{1}{7}=\dfrac{9}{63}~\textup{miles}.[/tex]

Now, since Lars started after 10 minutes, so distance run by Gavin in those 10 minutes will be

[tex]d_{G10}=\dfrac{10}{9}=\dfrac{70}{63}~\textup{miles}.[/tex]

Now, difference between Lars and Gavin's rate of runnings is

[tex]\dfrac{9}{63}-\dfrac{7}{63}=\dfrac{2}{63}.[/tex]

Therefore, the time taken by Lars to reach Gavin is given by

[tex]t=\dfrac{\frac{70}{63}}{\frac{2}{63}}=35.[/tex]

Thus, the required time is 365 minutes.