Chapter 11, Problem 105RE

To determine

What were the two speeds?

Answer to Problem 105RE

  $\boxed{36.67km/hr}$ , $\boxed{3.33km/hr}$

Explanation of Solution

Given information:

On a recent trip to the Cuyabeno Wildlife Reserve in the Amazon region of Ecuador, Mike took a $100-km$ trip by speedboat down the Aguarico River from Chritza to the Flotel Orellana. 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 $2.5hours$ and the return trip at $3hours$ . What were the two speeds?

Calculation:

Let time taken to downstream is $2.5hours$ and upstream is $3hours$

Now ,

Downstream speed $=\frac{100}{2.5}$

  $=40$

Upstream speed $=\frac{100}{3}$

  $=33.33$

Now speed of speedboat be considered as $x$ and current of the river be $y$ now downstream is given by addition of both speed of speedboat and current of the river,

  $x+y=40$

Upstream is given by difference of both,

  $x-y=33.33$

Let the system of two linear equations be formed as,

  $\{\begin{array}{l}x+y=40\\ x-y=33.33\end{array}$

Now add both the equations to eliminate the $y$ .

  $\begin{array}{l}\underset{\_}{\begin{array}{l}x+y=40\\ x-y=33.33\end{array}}\\ 2x=73.33\\ x=36.665\end{array}$

Now put $x=36.665$ in first equation,

  $\begin{array}{l}36.67+y=40\\ y=40-36.67\\ y=3.33\end{array}$

Hence the speed of speedboat and river current is $\boxed{36.67km/hr}$ , $\boxed{3.33km/hr}$