A person covers 1/10, 1/6, and 1/5 of the total distance at speeds of 3 km/h, 5km/h and 6 km/h, respectively. The remaining 16 km she covers at a speed of 16 km/h. How long does she take to travel the total distance?

Correct option is C

Given:

• A person covers:
• 1/10 of the total distance at 3 km/h
• 1/6 of the total distance at 5 km/h
• 1/5 of the total distance at 6 km/h
• The remaining 16 km is covered at 16 km/h
• We need to find the total time taken to travel the whole distance

Formula Used:

Time = Distance / Speed

Solution:

Let the total distance be D km

Step 1: Add up the fractional distances

1/10 + 1/6 + 1/5
→ Take LCM of 10, 6, and 5 = 30
→ Convert all to like fractions:
= 3/30 + 5/30 + 6/30 = 14/30
So, 14/30 of the total distance is covered in the first 3 parts.

Step 2: Remaining distance = 1 − 14/30 = 16/30 = 8/15 of D
We are told that this remaining distance = 16 km
So, 8/15 of D = 16 km
Now solve:
D = (16 × 15) ÷ 8 = 30 km

So, total distance = 30 km

Now calculate time for each segment:

1. First segment:
   Distance = 1/10 of 30 = 3 km
   Speed = 3 km/h → Time = 3 ÷ 3 = 1 hour
2. Second segment:
   Distance = 1/6 of 30 = 5 km
   Speed = 5 km/h → Time = 5 ÷ 5 = 1 hour
3. Third segment:
   Distance = 1/5 of 30 = 6 km
   Speed = 6 km/h → Time = 6 ÷ 6 = 1 hour
4. Last segment:
   Distance = 16 km
   Speed = 16 km/h → Time = 16 ÷ 16 = 1 hour

Total time = 1 + 1 + 1 + 1 = 4 hours

Final Answer: (C) 4 hours