### A man covers half part of a certain distance at 45 km/hr. He covers 40 percentage of remaining distance at the speed of 8 km/hr and covers rest of the distance at the speed of 24 km/hr. What is the average speed for the entire journey?

a) 164/7 km/hr

b) 144/7 km/hr

c) 156/7 km/hr

d) 128/7 km/hr

Ans : b) 144/7 km/hr

Solution :

Let’s assume the total distance is ( 2D ).

### Step 1: First part of the journey

The man covers half of the total distance, i.e., ( D ) at a speed of 45 km/h.

- Distance covered = ( D )
- Speed = 45 km/h
- Time taken for this part:

### Step 2: Second part of the journey

Now, 40% of the remaining distance is covered at 8 km/h. The remaining distance after the first part is ( D ), and 40% of this distance is ( 0.4D ).

- Distance covered = ( 0.4D )
- Speed = 8 km/h
- Time taken for this part:

### Step 3: Third part of the journey

The rest of the remaining distance is covered at 24 km/h. The remaining distance after the second part is ( 0.6D ).

- Distance covered = ( 0.6D )
- Speed = 24 km/h
- Time taken for this part:

### Step 4: Total time taken

The total time taken is the sum of the time taken for each part:

To simplify, take the LCM of 45, 20, and 40, which is 360:

So, the total time taken is:

### Step 5: Total distance covered

The total distance is ( 2D ).

### Step 6: Calculate the average speed

The average speed is given by:

Thus, the average speed for the entire journey is 144/7** km/h**.