If I walk at 5 km/hour, I miss a train by 7 minutes. However, if I walk at 6 km/hour, I reach the station 5 minutes before the departure of…

We have $(Speed = \frac{{distance}}{{time}})$

Hence we have Distance = Speed × Time

We have S1 and T1 be the speed and time taken when I walk at 5 kmph.

And S2 and T2 be the speed and time taken when I walk at 6 kmph.

Let time taken by man travelling at his usual speed = m minutes.

⇒ S1 × T1 = S2 × T2

⇒ 5 × (m + 7) = 6 × (m – 5)

⇒ 5m + 35 = 6m – 30

⇒ 6m – 5m = 30 + 35

⇒ m = 65 minutes.

∴ Distance travelled = 5 × (65 + 7)/60 = 5 × 72/60 = 6 km