Answer:
1 hour
Step-by-step explanation:
You want the shortest time required to get between opposite corners of a 2 mile square lake if the man walks at 4 mph and swims at 2 mph.
The land distance around two sides of the lake is 2+2 = 4 miles. At a walking speed of 4 mph, walking the entire distance would take ...
time = distance/speed
time = (4 mi)/(4 mi/h) = 1 h
The shortest distance across the lake that the man could swim is 2 miles (the length of one side). At 2 mph, that would take ...
(2 mi)/(2 mi/h) = 1 h
After having swum 2 miles, the man would still have some distance to walk. The total time involving any swimming would be more than 1 hour.
Walking the whole distance takes the shortest time.
The minimum time for the trip is 1 hour.
__
Additional comment
If swimming is involved, the shortest time would be about 1.366 hours. That is the time for the path leaving at an angle of 30° from the shore.
