If I walk at 5 km/hour; I miss a train by 7 minutes. If however, I walk at 6 km/hour I reach the station 5 minutes before the departure of the train. Then the distance between my house and the station is

the difference in time is 12 minutes

since time = distance/speed,

d/5 = d/6 + (12/60)
d = 6

check:

6km at 6km/hr = 1 hour
6km at 5km/hr = 1.2 hours = 1 hr 12 min

should it be this

d/5 = d/6 + (12/60)
or
d/5 - d/6 = (12/60)

Umm, looks the same to me.

a = b+c
is the same as
a-b = c

To find the distance between your house and the station, we can use the formula:

Distance = Speed × Time

Let's calculate the time it took for you to walk to the station at 5 km/hour and 6 km/hour:

At 5 km/hour:
Time = 7 minutes = 7/60 hours (since there are 60 minutes in an hour)
Speed = 5 km/hour
Distance = Speed × Time = 5 × (7/60) = 35/60 km

At 6 km/hour:
Time = 5 minutes = 5/60 hours
Speed = 6 km/hour
Distance = Speed × Time = 6 × (5/60) = 5/6 km

So, the distance between your house and the station is approximately 35/60 km (or approximately 0.583 km) when walking at 5 km/hour, and approximately 5/6 km (or approximately 0.833 km) when walking at 6 km/hour.