Let
𝑤
w represent the woman’s age and
𝑑
d represent the daughter’s age.

From the problem statement, we have two pieces of information:

The average age of the woman and her daughter is 16 years.
The ratio of their ages is 7 : 1.
Firstly, we set up the equations based on the information given:
𝑤
+
𝑑
2
=
16
2
w+d
​
=16
Multiply both sides by 2 to eliminate the fraction:
𝑤
+
𝑑
=
32
w+d=32

To determine how many minutes the train stops on average per hour, we need to find the difference in time taken between traveling without stoppages and traveling with stoppages over a distance of 100 km (assuming a convenient distance for calculation).

Time taken without stoppages:
Speed = 50 km/h
Distance = 100 km
Time = Distance / Speed = 100 km / 50 km/h = 2 hours

Time taken with stoppages:
Speed = 40 km/h
Distance = 100 km
Time = Distance / Speed = 100 km / 40 km/h = 2.5 hours

Difference in time = Time with stoppages – Time without stoppages
Difference in time = 2.5 hours – 2 hours = 0.5 hours

Convert the difference in time from hours to minutes:
0.5 hours × 60 minutes/hour = 30 minutes

Therefore, the train stops on average for 30 minutes per hour.