Though Pat's dog runs 2m/sec slower than Pat, the dog runs three times as fast as Lee. If Lee runs at x m/sec, and Pat races Lee,then, after 10 seconds, Pat will be ??? m ahead of Lee.

d = p-2

d = 3x

p-2 = 3x
p = 3x+2

So, after 10 seconds,
Lee has run 10x meters
Pat has run 10(3x+2) = 30x+20

So, Pat is 20x+20 meters ahead of Lee

To solve this problem, we need to determine the speeds of the dog and Lee relative to Pat, and then use that information to calculate how far ahead Pat will be after 10 seconds.

Let's start by assigning variables to the speeds of Lee and Pat's dog relative to Pat. According to the problem, the dog runs 2m/sec slower than Pat, and the dog runs three times as fast as Lee. So, if we let Pat's speed be represented by P, the dog's speed would be P-2, and Lee's speed would be (1/3)P.

Now, let's calculate how far each person will have traveled after 10 seconds. We can use the formula Distance = Speed × Time for each of the three individuals.

For Pat:
Distance_Pat = P × Time = P × 10 = 10P

For the dog:
Distance_Dog = (P-2) × Time = (P-2) × 10 = 10P - 20

For Lee:
Distance_Lee = (1/3)P × Time = (1/3)P × 10 = (10/3)P

Finally, to find Pat's lead over Lee after 10 seconds, we subtract Lee's distance from Pat's distance:
Lead = Distance_Pat - Distance_Lee = 10P - (10/3)P = (30/3)P - (10/3)P = (20/3)P

So, after 10 seconds, Pat will be (20/3)P meters ahead of Lee.

Remember, the exact value of Pat's lead depends on the value of P, which represents Pat's speed.