Chapter 7.1, Problem 51E

Solution

To calculate: The Hank’s rowing speed and the speed of the current.

The Hank’s rowing speed and the speed of the current are 3.56 mi/hr and 1.06 mi/hr.

Given Information:

The distance travelled by the Hank is 1 mi. The time taken against the stream is 24 min and in downstream is 13 min.

Calculation:

Consider the given information,

Suppose that the Hank’s rowing speed and the speed of the current be $x$ and $y$ respectively.

The time taken against the stream is 24 min and in downstream is 13 min. It implies,

  $\begin{array}{c}\frac{1}{x-y}=\frac{60}{24}\\ x-y=\frac{60}{24}\end{array}$   .....,. (1)

And,

  $\begin{array}{c}\frac{1}{x+y}=\frac{60}{13}\\ x+y=\frac{60}{13}\end{array}$   .....,. (2)

Adding equation (1) and (2).

  $\begin{array}{c}2x=\frac{60}{24}+\frac{60}{13}\\ x=\frac{37\times 60}{24\times 13\times 2}\\ x=3.56\text{ mi/hr}\end{array}$

Substitute $x$ in equation (1).

  $\begin{array}{c}3.56-y=\frac{60}{24}\\ y=3.56-2.5\\ y=1.06\text{ mi/hr}\end{array}$

Therefore, Hank’s rowing speed and the speed of the current are 3.56 mi/hr and 1.06 mi/hr.