Chapter 4.8, Problem 13P

To determine

To calculate: The distance travelled to reach the place of appointment.

Answer to Problem 13P

The total distance travelled to reach place of appointment is $165\text{km}$ .

Explanation of Solution

Given information:

Gina leaves now and drives at $66\text{km}/\text{h},$ and reaches in time for her appointment.

Gina takes lunch first and leaves in 40 minutes, and drives at $90\text{km}/\text{h}$ to make her appointment.

Let the time taken by Gina to reach Alton at the speed of $66\text{km}/\text{h}=t$

When Gina has lunch first and leaves in 40 min:

since, $40\text{min}=\frac{40}{60}h$

The time taken by Gina to reach Alton at the speed of $90\text{km}/\text{h}=t-\frac{40}{60}$

As, distance =speed $\times$ time

So, distance travelled by Gina in first case: $66t$

And, distance travelled by Gina in second case: $90\left(t-\frac{40}{60}\right)$

Since, both distances are equal,

  $\begin{array}{l}66t=90\left(t-\frac{40}{60}\right)\\ \Rightarrow 66t=90\left(t-\frac{40}{60}\right)\\ \Rightarrow 66t=90\left(t-\frac{2}{3}\right)\\ \Rightarrow 66t=90\left(\frac{3t-2}{3}\right)\\ \Rightarrow 66t=90\times \frac{3t-2}{3}\\ \Rightarrow 66t=30(3t-2)\\ \Rightarrow 66t=90t-60\\ \Rightarrow 90t-66t=60\\ \Rightarrow 24t=60\\ Or,t=\frac{5}{2}\end{array}$

As, distance travelled by Gina is given by $66t$

Therefore, the total distance travelled by the Gina is $66\left(\frac{5}{2}\right)=165\text{km}$ .