Question

Drew wants to get back to his campsite on the beach as fast as possible. He is swimming at a point in the water that is 300 feet from the shore at its closest distance, and his campsite is 3000 feet down the (perfectly straight) shore from there. In order to minimize his time, he wants to swim to some point (x) on the shore and then run the remaining distance. (x = 0 means he’s swimming the 300 feet directly to shore, and then running the 3000 feet to his campsite, whereas x = 3000 means he is swimming directly to his campsite and will not run at all.) He runs at the rate of 16 feet per second, and swims at the rate of 4 feet per second. What should the value of x be to minimize his time?

Answer 1

SOLUTION-:

The man swims to some point ( x ) on the shore & then run the remaining distance to the campsite (3000-x) feet

Clearly the running speed of the man (16 feet per second ) is greater than the swimming speed (4 feet per second).

time vs x equation of the man is (using speed, distance and time relation)

by solving we get

------------------------------------------- equation (i)

Clearly from the above equation (i) time (t) is minimum at x =0 because x can never be negative it means that the man swims to the shore that is 300 feet and then run to the campsite 3000 feet.

you can also understand this from his speed because his running speed is 4 times to that of swimming speed.