# While covering a distance of 24 km, a man notices that after walking for 1 hour

While covering a distance of 24 km, a man notices that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. His speed of walking is

- 9 km/hour
- 6 km/hour
- 10 km/hour
- 8 km/hour

Let the speed be x km/hr.

Then, distance covered in 1 hr. 40 min. = 5x/3 km.

Remaining distance = (24 – 5x/3) km.

⇒ 5x/3 = 5/7(24 – 5x/3) ⇔ x = 6

Hence, speed = 6 km/hr

**Answer: (2) 6 km/hr**

**Solution:-**

Let the speed be x km/hr.

Then, distance covered in 1 hr: 40 min

1 2/3 hrs = 5x/3 km.

Remaining distance = [24-5x/3] km.

Therefore, 5x/3 = 5/7[24-5x/3] ⇔ 5x/3 = 5/7[72-5x/3] ⇔ 7x = 72-5x

= 12x = 72

=> x = 6

Hence, speed = 6 km/hr = [6x 5/18] m/sec = 5/3m/sec = 1 2/3 m/sec

3. If a man walks at athe rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.

Sol. Let the required distance be x km.

Difference in the times taken at two speeds = 12 min = 1/5 hr.

Therefore, x/5 – x/6 = 1/5 => 6x – 5x = 6

=> x = 6.

Then, the required distance is 6 km/hr.

Hence, the correct answer is option (2) 6 km/hr.