LOL. loved your problem, it was so cute.
anyway yes you are right. it should be picked up at point P.
A snail, who can travel at 3 km/h hour is 10 km from the nearest point P on a straight highway. He wishes to travel to a point Q, 50 km along the highway from P, and she can arrange to have a turtle pick her up anywhere along the highway. The turtle travels at 15 km/h. What point on the highway should the snail head for as to arrive at Q in the shortest possible time?
Wouldn't the snail want to be picked up at point P to get there the quickest?