A boy, a girl and a dog are standing together on a long, straight road. Simultaneously, they all start walking in the same direction: The boy at 4 mph, the girl at 3 mph, and the dog trots back and forth between them at 10 mph. Assume all reversals of direction instantaneous.
In one hour, where is the dog and in which direction is he facing?
The very confused dog ends 3 + x from the starting point.
He has travelled for time t1 towards the boy and for time t2 towards the girl.
Therefore, 10 t1 - 10 t2 = 3 + x
Considering relatives speeds t1/t2 = 13/6
t1 = 1- t2
Therefore, 6 - 6 t2 = 13 t2
t2 = 6/19, t1 = 13/19
70/19 = 3 + x
x = .68
The dog is .68 miles from the girl.
What direction is he facing?
Let me think about that!