Aptitude - Time and Distance - Discussion

Thanks for your explanation @Sajan.

Total journey:: 10hr.

1st half journey by 21km/hr = 21 * 5 = 105km.
2nd half journey by 24km/hr = 24 * 5 = 120 km.
So, 105+120 = 225km.

As simple as it looks like:
2 * (10 * 21 * 24)/(21 + 24)
= 224 km.

According to me,

It is clear that first half hour the speed is 21 so total distance would be 21 * 5 = 105 km
And in second-hour distance would be 24 * 5 = 120 km,
So, the Total distance be 105 + 120 = 225 km.

[ ................................10hrs........................................]
5hrs 5hrs
/-------------------------------/-----------------------------------/

[speed21kmph...............] [....speed24kmph..................]


So, here clearly we know time and speed.

V = D/T
D = VT

Take 1st half D = 21 * 5 = 105kmph----------> 1
Take 2nd half D = 24 * 5 = 120kmph----------> 2


Total journey means add of 1st and 2nd half.

Total distance D = 105 + 120.
= 225kmph.

d = (2 * T * x * y)/(x + y) formula can also be used where x and y are two different speed.

Given,
Total time = 10 hours.
Speed 1(u)= 21 km/hr.
Speed 2 (v)= 24 km/hr.
Distance = ?

We know,
Average speed = 2uv/u + v.
= 2 * 21 * 24/ 21 + 24.
= 22.4 km/hr.

Now,
Distance = Speed * Time.
= 22.4 * 10
= 224 km which is the required answer.
It's as simple as that.

It is the first half of the distance. i.e x/2 not half of the time i.e 5 hours. So we cannot take 5 hours and multiply it with 21 and 24.

Please explain the first line of the solution.

Thank you so much @Sakthivel.