Chapter 2, Problem 15Q

You travel from point A to point B in a car moving at a constant speed of 70 km/h. Then you travel the same distance from point B to another point C, moving at a constant speed of 90 km/h. Is your average speed for the entire trip from A to C equal to 80 km/h? Explain why or why not.

To determine

Whether the average speed for the entire trip is $\text{80 km/h}$ or not.

Answer to Problem 15Q

Solution:

No

Explanation of Solution

Given:

The distance from A to B and B to C is same.

The speed of the car from point A to B is $70\text{km/h}$ .

The speed of the car from point B to C is $90\text{km/h}$ .

Formula Used:

  $\text{Average Speed =}\frac{\text{Total}\text{Distance}}{\text{Total}\text{time}}$

Calculation:

If the distance from A to B and B to C is same, let it be x km than total distance is equal to 2x km.

Time to cover distance from A to B $=\frac{x}{70}$

Time to coverdistance from B to C $=\frac{x}{90}$

Total time $=\frac{x}{70}+\frac{x}{90}$

  $\begin{array}{l}\text{Average speed =}\frac{2x}{\frac{x}{70}+\frac{x}{90}}\\ \text{Average speed =}\frac{2x\times 6300}{160x}\\ \text{Average speed =78}\text{.75}\text{km/h}\end{array}$

Conclusion:

Thus, the average speed is found to be less than 80 km/hr that is 78.75 km/hr.