Chapter 5.8, Problem 17P

To determine

To find how far she drive at each speed if the entire trip took her $2h40\min$

Answer to Problem 17P

The distance travelled is $75km\text{at}45km/hr$ and remaining $75km\text{at}75km/hr$

Explanation of Solution

Formula:

Given that total trip of 150 km at $45km/h$ and the rest of the trip at $75km/h$ in $(2h40\min )$

Formula:

  $\text{distance=speed}\times \text{time}$

Convert :

  $\left(2h40\min =2\times \frac{40}{60}=\frac{8}{3}h\right)$

Let total time be x

First, to determine the distance of speed $45km/h$ in x hour

  $speed\times time=45\times x=45x\mathrm{...............}(i)$

Now, determine the remaining distance of the have speed $75km/h$ in total $(2h40\min -x)$ .

  $speed\times time=75\times \left(\frac{8}{3}-x\right)\mathrm{...............}(ii)$

Thus , the total distance travelled is the sum of the distance traveled at $45km/h$ and $75km/h$

Now, Add equation ( i ) and equation ( ii )

  $\begin{array}{c}45x+75\left(\frac{8}{3}-x\right)=150\\ 45x+200-75x=150\\ -30x=-50\\ x=5/3h\end{array}$

Hence, the distance of speed $45km/h$ in $5/3h$$\Rightarrow$$45\times \frac{5}{3}=75km$

and distance of speed $75km/h$ in $\left(\frac{8}{3}-\frac{5}{3}\right)$$\Rightarrow$$75\times \frac{1}{3}=75km$