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

Solution:

  $s=4$ mph(Pamels speed in still water).

  $c=1$ mph(speed of the current).

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 " $c$ ".

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

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

Adding both equations we have,

  $2s=8$

  $s=4$ mph(Pamels speed in still water).

since $s+c=5$ mph we have,

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