Velocity distance problem?

Question

A woman and her dog are out for a morning run to the river, which is 4.0 km away. The woman runs at 2.5 m/s in a straight line. The dog is unleashed and runs back and forth at 4.5 m/s between the owner and the river, until the woman reaches the river. What is the total distance run by the dog?

Answer 1

After trying to solve this multiple times, I've come to a simple conclusion. The dog is constantly moving at a velocity of 4.5(m/s). Distance is time*velocity. The dog is in motion until the lady reaches the end. If we use an inversion of that formula, we get time=distance/velocity.

4000(m)/2.5(m/s) = 1600 seconds.
(time it takes her to reach the river)
1600(s)*4.5(m/s)=7200 meters or 7.2km
(that time multiplied by the dogs velocity to figure distance)

So, after failed attempts using calculus and other math that is unnecessary, we've come to the answer of 7.2km of distance covered by the dog. Hope this helps you out!

Answer 2

Of course, assuming instantaneous turn-around....
The time for the woman to reach the river is
t = s/v.

The distance the dog runs in that time is
s = vt (v now being the velocity of the dog), so

s = (4.0 km)(4.5 m/s)/(2.5 m/s)
s = 7.2 km