Chapter 6.4, Problem 5STP

For Exercises $1-5,$ choose the correct letter.

A kayaker paddles upstream for 1.5 hours, then turns his kayak around and returns to his tent in 1 hour. He travels 3 miles each way. What is the rate of the river’s current?

A. $0.5\text{mi}/\text{h}$

B. 2 $\text{mi}/\text{h}$

C. $1\text{mi}/\text{h}$

D. $1.5\text{mi}/\text{h}$

To determine

To identify correct answer:The rate of river current.

Answer to Problem 5STP

Option (A.) 0.5mi/h is the rate of the river current.

Explanation of Solution

Given information:

Time taken by kayaker when paddles upstream=1.5 hours

Time taken kayaker when returning to tent=1 hour

Distance of the river= 3miles

Formula used: $speed= \frac{distance}{time}$

Let us consider,

Average speed = r

Rate of river current= c

Now, speed of kayaker when paddles upstream $= \frac{distance}{time} =\frac{3miles}{1.5hr}=2mph,and$

Speed of kayaker when returning to tent $=\frac{distance}{time}=\frac{3miles}{1hr}=3mph.$

We know that,

  $\begin{array}{l}r-c=2mph\\ r+c=3mph\\ \overline{2r=5mph}\\ r=\frac{5}{2}\\ r=2.5mph\end{array}$ (using elimination method)

Now putting the value of above equation, we get-

  $\begin{array}{l}r-c=2mph\\ 2.5-c=2mph\\ -c=2-2.5\\ -c=-0.5\\ c=0.5mph\end{array}$

So, Option (A.) 0.5mi/h is the rate of the river current.