Chapter SH, Problem 8.19EP

a.

To determine

To write an expression for Natalie’s time.

Answer to Problem 8.19EP

  $t_1=\frac{60}{N}\text{ hour}$

Explanation of Solution

Given:

Natalie can bike $10$ kilometers per hour faster than Aaron. Natalie travels $60$ km and Aaron has gone $40$ kilometers.

Calculation:

Let the Natalie’s speed be $N$ km/hour and thus Aaron’s speed will be $N-10$ kilometers per hour.

Let the time take by Natalie be $t_1$

  $t_1=\frac{60}{N}\text{ hour}$

Hence, the expression for Natalie’s time $t_1=\frac{60}{N}\text{ hour}$ .

b.

To determine

To write an expression for Natalie’s time.

Answer to Problem 8.19EP

  $t_2=\frac{40}{N-10}\text{ hour}$

Explanation of Solution

Given:

Natalie can bike $10$ kilometers per hour faster than Aaron. Natalie travels $60$ km and Aaron has gone $40$ kilometers.

Calculation:

Let the Natalie’s speed be $N$ km/hour and thus Aaron’s speed will be $N-10$ kilometers per hour.

Let the time take by Aaron be $t_2$

  $t_2=\frac{40}{N-10}\text{ hour}$

Hence, the expression for Natalie’s time $t_2=\frac{40}{N-10}\text{ hour}$ .

c.

To determine

To write and solve the rational equation to determine and solve the speed of each biker.

Answer to Problem 8.19EP

The Natalie’s speed be $30$ km/hour and thus Aaron’s speed will be $20$ kilometers per hour.

Explanation of Solution

Given:

Natalie can bike $10$ kilometers per hour faster than Aaron. Natalie travels $60$ km and Aaron has gone $40$ kilometers.

Calculation:

Let the Natalie’s speed be $N$ km/hour and thus Aaron’s speed will be $N-10$ kilometers per hour.

Since the time taken by both is equal.

  $\begin{array}{l}{t}_1=t_2\\ \Rightarrow \frac{60}{N}=\frac{40}{N-10}\\ \Rightarrow \text{60}N-600=40N\\ \Rightarrow 20N=600\\ \Rightarrow N=30\\ \Rightarrow A=N-10=30-10=20\end{array}$

Hence, the Natalie’s speed be $30$ km/hour and thus Aaron’s speed will be $20$ kilometers per hour.