Q. 66 - Precalculus Enhanced with Graphing Utilities

Question

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.)

Step-by-Step Solution

Answer

Pamelas speed in calm water is 4 miles per hour and in the current it is 1 miles per hour.

Step 1: Given information

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

Step 2: Find the equations

Let x be the speed in still water and y be the speed of the current

Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. Hence we have,

$$\begin{gathered} x-y=\frac{15}{3} \\ x-y=5 \left(1\right) \end{gathered}$$

The return trip upstream takes 5  hours 

Therefore we get,

$$\begin{gathered} x+y=\frac{15}{5} \\ x+y=3 \left(2\right) \end{gathered}$$

Step 3: Solve the equations

To solve the equations Add the two equations

We get,

$x-y=5+x+y=32x=8$

Hence $x=4$

Also we have

$$\begin{gathered} x+y=5 \\ 4+y=5 \\ y=1 \end{gathered}$$

Step 4: Conclusion

Pamelas speed in calm water is 4 miles per hour and in the current it is 1 miles per hour.