Using for loop to print a time sequence

Use binary arithmetic operations for handling minutes and hours, namely modulo operator % and floor division //:

h = 13 
m = 36

for i in range(10):
    print("The train will leave at {}:{} ".format(h,m))
    h = h+((m+20)//60)
    m = (m+20)%60
    if h == 24:
        h = 0

Note the last two lines: you should check the hour value in order to come back to 0 when h==24.

You can use datetime module from standard library:

from datetime import timedelta, datetime

t = datetime(hour=13, minute=36, year=2019, month=6, day=9)

for i in range(5):
    print("The train will leave at {}:{} ".format(t.hour,t.minute))
    t += timedelta(minutes=20)

Prints:

The train will leave at 13:36 
The train will leave at 13:56 
The train will leave at 14:16 
The train will leave at 14:36 
The train will leave at 14:56 

A slight modified version of your code. Just check for the minutes using if. In case, minutes are more than 60, increase the hour by one and rewind the minutes back by subtracting 60

h = 13 
m = 36

for i in range(5):
    if 60 <= m:
        m = m-60
        h = h+1
    print("The train will leave at {}:{} ".format(h,m))       
    m = m + 20

# The train will leave at 13:36 
# The train will leave at 13:56 
# The train will leave at 14:16 
# The train will leave at 14:36 
# The train will leave at 14:56     

You should give the % operator a try.

The % operator is the modulo operator which you can easily think of as an operator that provides the remainder of the division between the left operand and the right one. Defining this operator can get a bit more technical if you did some group theory or abstract algebra in college.

Basically start at a given minute and increment by 20 minutes. Whenever the number of minutes passes 60 minutes then we need to increment the hour. But we need to reset the number of minutes. So the first time m reaches 76, we set it back to 76 - (1 * 60) = 16. Note that m will never go past 120 unless it is set to a number larger than 99 from the get go.

What I think you really want is this though

h = 13 
m = 36

for i in range(5):
    print("The train will leave at {}:{} ".format(h,m))
    m = m + 20
    if  m >= 60:
        h += 1
        m = m % 60

Output

# The train will leave at 13:36 
# The train will leave at 13:56 
# The train will leave at 14:16 
# The train will leave at 14:36 
# The train will leave at 14:56 

But you should probably also account for when h goes past 24. so if h >= 24: h = 0.

Once again the assumption is that you always begin with m below 60.

Use the following if statement to check for hour change, I have changed the hour and minutes for double checking

h = 15 
m = 53

for i in range(5):
    print("The train will leave at {}:{} ".format(h,m))
    m = m + 20
    if m >= 60:
        h = h+1
        m-=60
        print("The train will leave at {}:{} ".format(h,m))
        m = m + 20

The execution will be:

The train will leave at 15:53 
The train will leave at 16:13 
The train will leave at 16:33 
The train will leave at 16:53 
The train will leave at 17:13 
The train will leave at 17:33 
The train will leave at 17:53 
The train will leave at 18:13