Chapter 11, Problem 59RE

To determine

To find: The speed of boat and current.

Answer to Problem 59RE

Speed of boat was 36.67 km/h

Speed of current was 3.33 km/h

Explanation of Solution

Given: On a recent trip to the Cuyabeno Wildlife Reserve in the Amazon region of Ecuador, Mike took a 100-kilometer trip by speedboat down the Aguarico River from Chiritza to the Flotel Orellena. As mike watched the Amazon unfold, he wondered how fast the speedboat was going and how fast the current of the white-water Aguarico River was.

Mike timed the trip downstream at 2.5 hours and the return trip at 3 hours.

Formula Used : $\text{Speed = }\frac{\text{Distance}}{\text{Time}}$

Let speed of boat be $x\text{ km/h}$ and speed of current be $y\text{ km/h}$ .

For downstream:

Net speed $=\left(x+y\right)\text{ km/h}$

Time $=2.5\text{}\text{hours }$

Distance covered $100\text{ km}$

  $\begin{array}{c}\text{Speed = }\frac{\text{Distance}}{\text{Time}}\\ x+y=\frac{100}{2.5}=40\mathrm{...}\left(i\right)\end{array}$

For upstream:

Net speed $=\left(x-y\right)\text{ km/h}$

Time $=3\text{}\text{hours }$

Distance covered $100\text{ km}$

  $\begin{array}{c}\text{Speed = }\frac{\text{Distance}}{\text{Time}}\\ x-y=\frac{100}{3}\mathrm{...}\left(ii\right)\end{array}$

Add equation $\left(i\right)\text{ and }\left(ii\right)$

  $\begin{array}{c}2x=40+\frac{100}{3}=\frac{220}{3}\\ x=\frac{110}{3}\approx 36.67\text{}\text{km/h}\end{array}$

Put $x=36.67\text{ in }\left(i\right)$

  $\begin{array}{c}36.67+y=40\\ y=\frac{10}{3}\approx 3.33\text{ km/h}\end{array}$

Hence, speed of boat was 36.67 km/h and speed of current was 3.33 km/h.