Chapter 9.6, Problem 16OE

To determine

To find: The corresponding statement of the equation in option and the rate is in km per hour.

Answer to Problem 16OE

The option $\text{a}$ is correct the rowboat is travelled $\text{20}$ km upstream and $\text{30}$ km downstream in $\text{2}$ hours.

Explanation of Solution

Given:

  $\frac{\text{30}}{\text{r+c}}+\frac{\text{20}}{\text{r-c}}=2$ .

Concept used:

If the thing is going against the gravity is taken as $\text{-ive}$ .

Vector formula:

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{+2ABcosθ}$ .

If the direction of any against the gravity means it make ${\text{180}}^0$ with the gravity.

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{-2AB}$ .

  $\text{R=A-B}$ .

  $\text{distance=rate}\times \text{time}$ .

Calculation:

According to the given equation:

  $\frac{\text{30}}{\text{r+c}}+\frac{\text{20}}{\text{r-c}}=2$ .

Here $\text{r+c}$ is the rate of the boat with the current so the boat is travelling downstream.

  $\text{r-c}$ is travelling upstream so the equation is saying that the combine time it takes to travel $\text{30}$ km downstream and $\text{20}$ km upstream is $\text{2}$ hours.

which matches with option $\text{a}$ .

Hence the option $\text{a}$ is correct the rowboat is travelled $\text{20}$ km upstream and $\text{30}$ km downstream in $\text{2}$ hours.