A man rides at the rate of 18km/hr, but stops for 6 mins. To change horses at the end of every 7th km. The tme that he will take to cover a distance of 90km is

Options

A. 6 hrs
B. 6 hrs 12 min
C. 6hrs 18 min
D. 6hrs 24min

Answer

To solve the problem, we need to calculate the total time taken by the man to cover a distance of 90 km, considering his speed and the stops he makes to change horses.

### Step-by-Step Solution:

1. **Determine the Speed and Distance**:
- The man rides at a speed of 18 km/hr.
- The total distance to cover is 90 km.

2. **Calculate the Time Taken Without Stops**:
- Time = Distance / Speed
- Time taken to cover 90 km without any stops = 90 km / 18 km/hr = 5 hours.

3. **Determine the Number of Stops**:
- The man stops every 7 km.
- To find out how many stops he makes in 90 km, we divide the total distance by the distance after which he stops.
- Number of stops = 90 km / 7 km = 12.857. Since he can only stop at complete intervals, he will stop 12 times (after 7 km, 14 km, ..., up to 84 km).

4. **Calculate the Total Stopping Time**:
- Each stop takes 6 minutes.
- Total stopping time = Number of stops × Time per stop = 12 stops × 6 minutes = 72 minutes.

5. **Convert Stopping Time to Hours**:
- 72 minutes is equivalent to 72 / 60 = 1.2 hours or 1 hour and 12 minutes.

6. **Calculate the Total Time Taken**:
- Total time = Time taken without stops + Total stopping time
- Total time = 5 hours + 1 hour 12 minutes = 6 hours 12 minutes.

### Final Answer:
The total time that the man will take to cover a distance of 90 km is **6 hours and 12 minutes**.