Chapter 7, Problem 5MPS

To determine

To find: Total distance travelled by Mia is 30km..

Answer to Problem 5MPS

Let the Length of first piece: $3ft$

Let the Length of second piece: $9ft$

Explanation of Solution

Given information:

• Mia went downtown by bus, travelling at 60km/h, she walked home at 6km/h.
• Her total travelling time is 2.75h.

Formula used:

  $Speed=\frac{Distance}{Time}$

As Distance travel by Mia during going to downtown and coming back is same,

So,

During going to downtown:

Let time travel during going to downtown: $t$

Speed during going to downtown: $60km/h$

  $\begin{array}{l}60=\frac{Distance}{t}\\ distance=60t\mathrm{....}\left(1\right)\end{array}$

During walking, back to home:

Time travel to walk back home: $2.75-t$

Speed during walking back to home: $6km/h$

  $\begin{array}{l}6=\frac{Distance}{2.75-t}\\ distance=6\left(2.75-t\right)\\ distance=16.5-6t\end{array}$

Equating distance travelled in both journey:

  $\begin{array}{l}60t=16.5-6t\\ 60t+6t=16.5\\ 66t=16.5\\ t=\mathrm{0.25......}\left(2\right)\end{array}$

Putting value of t in eq.1

  $\begin{array}{l}distance=60t\\ distance=60\times 0.25\\ distance=15\end{array}$

distance will be multiplied by 2 to find total distance travelled:

  $\begin{array}{l}2d\\ =2\times 15\\ =30\end{array}$

Total distance travelled by Mia is 30km.