Chapter 11.6, Problem 16PPE

To determine

What is the speed of camper at the end of the summer?

Answer to Problem 16PPE

  $13.33mi/h$

Explanation of Solution

Given information:

A camper takes $2h$ to ride a bike around a reservoir at 10mi/h at the beginning of summer.

By the end of summer, she can ride around the reservoir in $1\frac{1}{2}h$

The time to travel around the reservoir varies inversely with the speed she pedals.

Concept Used:

• Speed, distance and time concept is used.

  $speed=\frac{dis\tan ce}{time}$

Calculation:

Speed of bike around a reservoir at the beginning of summer = 10mi/h.

Time taken = $2h$

As $speed=\frac{dis\tan ce}{time}$

  $speed\cdot time=dis\tan ce$

  $dis\tan ce=speed\cdot time$

Distance from house to lake = $10\cdot 2$

  $=20mi$

Time taken to ride a bike around a reservoir by the end of summer = $1\frac{1}{2}h$

As travel time varies inversely with the speed of the car.

  $\begin{array}{c}spee{d}_1\cdot tim{e}_1=spee{d}_2\cdot tim{e}_2\\ 10\cdot 2=spee{d}_2.1\frac{1}{2}\\ 20=\frac{3}{2}.spee{d}_2\\ spee{d}_2=\frac{40}{3}\\ spee{d}_2=13.33mi/h\end{array}$

speed of camper at the end of the summer = $13.33mi/h$