physics
posted by Laura .
A man jogs along at 1.2 m/s. His dog, playing 36 m behind him, waits for 5 s, then takes off after him at 3.1 m/s.
How far apart are they when the dog starts
after his master?
Answer in units of m.
If the man continues jogging, how long will
the dog have to run to catch up to his master?
Answer in units of s.
How far will the dog run?

How far does the man run in 5 s? That would be 1.2*5 = 6 meters. You have to add that to 36 meters, which was the initial distance the dog was behind. That makes 42 m makeup distance.
The intervening distance gets reduced at a rate 3.1  1.2 = 1.9 m/s
The dog catches up after
t = 42/1.9 = 22.1 s 
How far will the dog run?