Chapter 11.6, Problem 6CYP

To determine

To calculate: The expression for the total time for the trip.

Answer to Problem 6CYP

The required expression for the total time is $\frac{11}{1.2r}$ .

Explanation of Solution

Given information:

The distance between Lynbrook to Long Beach is 5 miles.

Speed of the train from Lynbrook to Long Beach is $r$ .

Formula Used:

Time requires to travel a distance $d$ moving with a velocity $v$ is

  $t=\frac{d}{v}$

Calculation:

It is given that the train travels 1.2 times faster returning from Long Beach.

Thus. Speed of the train from Long Beach to Lynbrook is $1.2r$ .

Let $t_1$ be the time required by the train to travel from Lynbrook to Long Beach.

Thus, find $t_1$ , use the formula $t=\frac{d}{v}$ .

  $t_1=\frac{5}{r}$  .... (1)

Let $t_2$ be the time required by the train to travel from Long Beach to Lynbrook.

Find $t_2$ , use the formula $t=\frac{d}{v}$ .

Thus, $t_2=\frac{5}{1.2r}$  .... (2)

Now, find the total time add (1) and (2).

  $\begin{array}{c}{t}_1+t_2=\frac{5}{r}+\frac{5}{1.2r}\\ =\frac{11}{1.2r}\end{array}$

Hence, the required expression for the total time is $\frac{11}{1.2r}$ .