21. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight?

1 hour? 2 hours? 3 hours? 4 hours?
3 hrs. and 4 hrs. are too large as the average speed is to be greater than 200 kmph.
Test 1 hr.
Time is 1 hr., so Normal speed is 600 kmph.
Slower speed is 400 kmph. and time is 1 hr 30 min.
So flight time increase is 30 min. and this fits the bill.

22. A man completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
[Note the simplification / solution below!]
  Let half the distance be d km.
d is calculated mentally! [Explanation below.]
Equating total travel time:

Multiply everything by 3:

Multiply everything by 7 x 8:
8d + 7d = 1680

Solving d = 112
Total journey is 224 km.
An Alternative Solution:
 'An Useful RULE':
If two equal distances are covered at two different speeds s1 and s2 the average speed for the whole (double distance) journey is
  av speed (1K)
Average speed for the total, 10 hrs. journey, is 22.4 kmph;
Total journey is 22.4 x 10 = 224 km.

23. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

70 kmph., 2) 75 kmph., 3) 84 kmph., 4) 87.5 kmph.
Speed of 2nd train is 400/4 = 100 kmph.
Using the ratio, speed of 1st train 7 of 8 parts;
seven-eighth of 100 = 87.5 kmph.

24. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
 Equal distances at different speeds:
Average speed is misc calc 01 (1K) kmph

A car travelling with Fr_5_7 (1K) of its actual speed covers 42 km in
1 hr 40 min 48 sec. Find the actual speed of the car.
One-Step Solution!
The beauty of the Calculation!!