# Two shepherds who were at a distance of 600m from each other begin to move towards each other at a speed

**Two shepherds who were at a distance of 600m from each other begin to move towards each other at a speed of 3 km per hour, simultaneously with the shepherds, their dog begins to run from one to another and back at a speed of 20 km per hour, this continues until they meet, determine the path and movement of the dog.**

1. Shepherds move in opposite directions at the same speed of 3 km / h. Consequently, the speed of their convergence is 6 km / h.

2. The distance that the shepherd must overcome is 600 m, i.e. 0.6 km. Knowing the speed and distance, we calculate the time by the formula:

t = S / V

t = 0.6 km / 6 km / h = 0.1 h

3. Let’s find out what distance the dog will cover during this time:

S = V × t

S = 20 km / h × 0.1 h = 2 km

4. Let’s find out how many times 0.6 km fits in 2 km:

2 / 0.6 = 3, (3)

3 × 0.6 = 1.8

2 – 1.8 = 0.2

3 full times with a remainder of 200 m

4. Since the number of times is odd, the dog ran towards the starting point at the moment the shepherds met.

600 – 200 = 400

Answer: the dog ran 2 km, being 400 m from the starting point