Chapter 11.1, Problem 66AYU

To determine

To find: Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela’s average speed in still water. How fast is the current? (Assume that Pamela’s speed is the same in each direction).

Answer to Problem 66AYU

$s=4\text{ mph}\left(\text{Pamels speed in still water}\right)$.

$c=1\text{ mph}\left(\text{speed of the current}\right)$.

Explanation of Solution

Given:

Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours.

Calculation:

Pamela requires 3 hours to swim 15 miles downstream in the Illinois river.

It is given that time $=3$ hrs, distance $=15$ miles.

So the rate $=\frac{\text{distance}}{\text{time}}=\frac{15}{3}=5\text{ mph}$.

The return trip upstream takes 5 hours.

It is given that time $=5$ hrs, distance $=15$ miles.

So the rate $=\frac{\text{distance}}{\text{time}}=\frac{15}{5}=3\text{ mph}$.

Let her swim speed be “$s$”.

Let her current speed be “$c$”.

$\text{Downstream}:s+c=5\text{ mph}$   -----1

$\text{upstream}:s-c=3\text{ mph}$   -----2

Adding both equations we have,

$2s=8$

$s=4\text{ mph}\left(\text{Pamels speed in still water}\right)$.

Since $s+c=5\text{ mph}$ we have,

$c=1\text{ mph}\left(\text{speed of the current}\right)$.