Ashish covers 72 km at a speed of 45 km/h by bike, 28 km at a speed of 4 km/h by bicycle, and another 160 km at a speed of 20 km/h by car. Find his average speed (in km/h) for the whole journey. (Rounded off to two decimal places)

To find Ashish's average speed for the whole journey, we use the standard formula for average speed:

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

Let's calculate the total distance covered and the total time taken for each part of the journey step-by-step:

Step 1: Calculate the total distance covered
The journey consists of three parts:
1. By bike: 72 km
2. By bicycle: 28 km
3. By car: 160 km

$\text{Total Distance}=72+28+160=260\text{km}$

Step 2: Calculate the time taken for each part of the journey
Time is calculated as distance divided by speed ($t=\frac{d}{v}$):

• Time taken by bike ($t_1$):
$t_1=\frac{72}{45}=1.6\text{hours}$

• Time taken by bicycle ($t_2$):
$t_2=\frac{28}{4}=7\text{hours}$

• Time taken by car ($t_3$):
$t_3=\frac{160}{20}=8\text{hours}$

Step 3: Calculate the total time taken
$\text{Total Time}=t_1+t_2+t_3=1.6+7+8=16.6\text{hours}$

Step 4: Calculate the average speed
Now, divide the total distance by the total time:
$\text{Average Speed}=\frac{260}{16.6}\approx \mathrm{15.66265...}\text{km/h}$

Rounding to two decimal places, we get 15.66 km/h.

Therefore, the correct option is 15.66.