A river is wide

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A river is

60\text{ m}

wide. A swimmer starts at point

S

on one bank and wishes to reach a point

T

that is

100\text{ m}

downstream on the opposite bank. The swimmer can travel at

2\text{ m/s}

in water and run at

5\text{ m/s}

on land along the far bank. Let

x

be the downstream distance (in meters) from the point directly opposite

S

to the landing point

L

on the far bank (so

0\le x\le100

). For which value of

x

will the total travel time from

S

T

be minimized? (a)

50\text{ m}

(b)

26\text{ m}

(c)

12\text{ m}

(d)

100\text{ m}