Sure, I can help you with that! Let's break down the problem step by step.
Daniel's pace is 1 lap per minute, and he has already completed 8 laps. So, the distance Daniel has covered is 8 laps.
Nick's pace is 5 laps per minute. Let's assume they both run for 't' minutes after Nick joins Daniel on the track. During this time, Nick would have run 5t laps.
Since they both cover the same distance at some point, we can set up an equation to solve for 't':
8 + 1t = 5t
By simplifying the equation, we get:
8 = 4t
Now, we can solve for 't' by dividing both sides of the equation by 4:
t = 8/4 = 2
Therefore, it will take 2 minutes for Daniel and Nick to run the same distance.
To find out how many laps each boy will have run, we can substitute the value of 't' back into one of the expressions.
Daniel will have run 8 + 1t = 8 + 1(2) = 8 + 2 = 10 laps.
Nick will have run 5t = 5(2) = 10 laps as well.
So, Daniel and Nick will both have run 10 laps when they have covered the same distance after 2 minutes.