Aptitude - Time and Distance - Discussion

Let the time for 1st half be x.
x.21 = (10-x).24
x = 80/15.
D = 80/15 X 21 X2
= 224km.

The right answer is 234 km.

I am not a mathematician. But, a question arises in me that is :

First half of 10 hours = 5 hours.
Second half of 10 hours = 5 hours.

Then, 5 Hours @ 21 KM Per hour = 21x5 = 105 km.
And nest 5 hours @ 24 KM per hour = 24x5 = 120 km.

Total (21x5) + (24x5) = 105 + 120 = 225.

So, why the answer is not 225 KM.

What would be the mistake here?

If there was no mention of first half and 2nd half of 10 hours, (i.e. 10 hours / 2 = 5 hours,) if it was only mentioned that first the person traveled @ 21 KM/hour and then 24 Km/per, then may be it would be solved using any time & distance formula.

Being a ordinary class student, this question has arisen in my mind.

May I kindly be helped with proper answer ?

Average speed = 2xy/x+y.

Here
X =21.
Y = 24.

Then, the average speed is;
2(21)(24)/45 = 22.4.

Average speed= total distance/total time.
22.4 = X/10,
224 = X,
Finally, the distance is 224.

In question, it was mentioned that the first half of the distance so for first half time can not be 5 hrs. For that reason those who are getting 225 will be wrong. If he will travel at 21 km/h ge will not reach half of the distance in 5 hrs.

Why can't the answer be calculated like average speed?

We sum up the speeds of 21 and 24, divide by 2, and use that speed in the formula.
Multiply 10 hours by 22.5 kmph and get 225 km!

@All.
Here I got a different answer. I am not getting it clearly. So, can anyone clarify this to me?

Since total distance is divided in two equal half part.

Therefor 10 can be written as 5+5 = 10.

Time = Distance/Speed (5 = x/2*21 and next 5 = x/2*24).

Place these value.

x/2*21 + x/2*24 = 10.

By solving x = 224.

Here, They Mentioned half of the journey.

They didn't mention half of the time.

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.

The easiest method is just take ratio as-

21:24=7:8(speed ratio) & sp is inversely proportion to time so 8:7(time ratio).
Now 8+7=15 portion =10hrs so 1 portion =2/3 hrs so 8 portion =16/3 hrs.
Now, dis=21*(16/3)=112(this is half dis).
So whole dis=112*2=224 km.