Page 103 - How To Solve Word Problems In Calculus

EXAMPLE 9
A river is 1 mile wide. Frank wants to get from point A to
point B on the opposite side of the river, 3 miles downstream.
If Frank can run 5 miles per hour and can swim 3 miles per
hour, what is the least amount of time in which he can get
from A to B?

Solution
Step1
Let C be the point on the other side of the river directly
opposite A. Let D be the point between C and B that Frank
should swim to; he will run the rest of the way to B. Let x be
the distance from C to D.

C x D 3 − x B

2 + 1
1
√ x

A

Steps 2 and 3
Since d = r × t, the time necessary to either run or swim
is determined by t = d/r.

√
2
d swim x + 1
t swim = =
r swim 3
d run 3 − x
t run = =
r run 5

The total time to go from A to B is t swim + t run so
√
2
x + 1 3 − x
t(x) = + . It is clear that 0 ≤ x ≤ 3.
3 5
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