A bus covers the first 50 km of its journey in 40 minutes and covers the remaining 75 km in 40 minutes. What is the average speed (in km/h) of the bus?

The correct answer is $93\frac{3}{4}$ km/h.

Step-by-Step Explanation:

To calculate the average speed of the bus, we use the fundamental formula for average speed:

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

Step 1: Calculate the Total Distance Covered
The journey is divided into two parts:
• Distance of the first part = 50 km
• Distance of the second part = 75 km

$\text{Total Distance}=50\text{km}+75\text{km}=125\text{km}$

Step 2: Calculate the Total Time Taken
The time taken for each part of the journey is:
• Time for the first part = 40 minutes
• Time for the second part = 40 minutes

$\text{Total Time}=40\text{min}+40\text{min}=80\text{minutes}$

Since the speed needs to be in kilometers per hour (km/h), we must convert the total time from minutes to hours by dividing by 60:

$\text{Total Time in hours}=\frac{80}{60}\text{hours}=\frac{4}{3}\text{hours}$

Step 3: Compute the Average Speed
Substitute the total distance and total time into the average speed formula:

$\text{Average Speed}=\frac{125}{\left(\frac{4}{3}\right)}=125\times \frac{3}{4}=\frac{375}{4}\text{km/h}$

Convert the improper fraction $\frac{375}{4}$ to a mixed number:
$375÷4=93$ with a remainder of 3.

$\text{Average Speed}=93\frac{3}{4}\text{km/h}$