This problem asks us to determine the average speed ($x$) of Bani while cycling. Here's how we solve it.

Step-by-Step Solution:

1. Given Data:

   • Speed from City X to City Y: $40 \, \text{km/h}$
   • Speed from City Y back to City X: $20 \, \text{km/h}$

2. Understanding the Concept: Average speed is not simply the arithmetic mean of the two speeds because Bani spends more time traveling at the slower speed. Instead, the average speed $x$ is calculated using the formula for average speed over a round trip:

   $x = \frac{2v_1v_2}{v_1 + v_2}$ where:

   • $v_1$ is the speed going to the destination (40 km/h),
   • $v_2$ is the speed returning from the destination (20 km/h).

3. Substitute the Values:

   $x = \frac{2 \times 40 \times 20}{40 + 20}$ $x = \frac{1600}{60} = 26.67 \, \text{km/h}$

So, the average speed $x$ is approximately 26.67 km/h.

Would you like more details on the steps or any clarifications?

Here are 5 related questions you might find helpful:

1. What is the formula for average speed for different types of trips?
2. Why doesn't arithmetic mean apply for average speed in this case?
3. How does time influence the calculation of average speed?
4. What if the distance between the cities was different for the return trip—how would you calculate the average speed then?
5. How does increasing the return speed affect the overall average speed?

Tip: When calculating average speed over varying speeds, always consider the time spent at each speed!