Smriti goes to a shopping mall at a speed of 21 km/hr and returns at a speed of 69 km/hr. Find her average speed (in km/hr) for the entire trip.

The correct answer is 32.2.

Step-by-Step Explanation:

When an object travels equal distances at two different speeds, say $a$ and $b$, the average speed for the entire journey is given by the harmonic mean of the two speeds.

$\text{Average Speed}=\frac{2\times a\times b}{a+b}$

Given in the problem:
Speed while going to the shopping mall ($a$) = 21 km/hr
Speed while returning ($b$) = 69 km/hr

Now, substitute the values into the average speed formula:

$\text{Average Speed}=\frac{2\times 21\times 69}{21+69}$

Simplify the denominator:

$21+69=90$

Now, calculate the numerator:

$2\times 21\times 69=2898$

Divide the numerator by the denominator:

$\text{Average Speed}=\frac{2898}{90}=32.2\text{km/hr}$

Thus, her average speed for the entire trip is 32.2 km/hr.