Answer: 5km by straight line, 7km by route.
Explanation:
The distance by route is 3km south and then 4km east, notice that the distances are perpendicular to each other, so the total distance traveled (by a straight line) is:
D = √((3km)^2 + (4km)^2) = √(9km^2 + 16km^2) = (√25)km = 5km
So the distance by a straight line that he needs to go back to where he started is 5km, and if he wants to get back by route, he must do 4km to the west and then 3km to the north, so a total of 7km
