Aptitude - Time and Distance - Discussion

I didn't understand this, can you explain this question?

Hear if total distance is X.

And hear fix first 1/2 at fix speed and another half at other fix speed.

So we can assume avg speed so [ speed (1) + speed (2) ] / 2 so we get avg speed for a total this x.

Then for 10 hr final answer is *10 so we get 225.

If the answer is 224,(DISTANCE BASED).

If you think total journey 224, then half of the journey is 112 KM, travels at the speed 21 KMPH means time taken to complete 1st half is 112/21=5.33333.. hrs.

For 2nd half journey, i.e 112 KM travels at the speed 24 KMPH, the time taken for this is 112/24=4.666666...hrs.

If we add both times it will be so much near to 10 hours, but not exactly 10 hours.

If we go through following way,(TIME-BASED).its gonna be right.

Total journey is 10 hours.half of the journey is 5 hours for the 1st half journey at the speed 21 KMPH means distance travelled in 1st half is 21*5=105, in the same way, distance travelled in 2nd half is 24*5=120.

So, total distance 105+120=225km.

Here, They Mentioned half of the journey.

They didn't mention half of the time.

Clearly, 10hrs is there, why they taken time is X hrs? please explain me.

Thank you @Jing.

For these kind ques, there is a simple formula i.e.

Distance= 2* time* product of speeds / addition of speeds

ans: distance = 2*10*21*24 /21+24.
=10080/45,
= 224 km.

Distance =speed*time.
So x=(21*5)+(24*5)=225.
X=225 km.

Why should it not be like this? Please explain.

It's quite simple,

Avg speed is the harmonic mean of those two speeds (as the distances are same)
So, avg speed would be , avg speed = 2*21*24 / (21+24) = 22.4 kmph
Now, time is given as 10 hours.

So, d = s * t
d = 22.4 *10
d = 224 km.

d=s*t.

Let the total distance be 2d.
for first part,
distance=d
time taken be=t
speed=21 km/hr.

for the second part
dis=d
time=10-t
speed=24 km/hr

Since distance covered is equal
so,
d for 1st half=d for the 2nd half
t*21=(10-t)*24

Using this I calculated the time for the individual half's through get the distance.

but I am not able to get the correct answer. Can anyone tell me the logic behind that?