Aptitude - Time and Distance - Discussion

@Mohammed is wrong.

Because,
Average speed is the weighted average with the time traveled at the different speeds being the weight & not the distance traveled at different speeds.

Hey guys. There's a easy way to solve this.

When distance is equal in both halves then use this formula,

2*u*v/u+v(where u and v are the given speeds pertaining to given distances).

Here u is 21 and v is 24.

So according to our formula we have,

2*21*24/21+24=1008/45=112/5=22.4.

So now according to TSD formula,

Speed = distance /time.

Hence 22.4 = d/10.

Thus d = 22.4*10 = 224kms

@Muhammed way is incorrect because, you can't just assume that first half equals second half equals 5 hours. Your speed is different in the two halves of the journey. You are going slower at first half but faster at second half. So you are taking a bit more than 5 hours in first half, and a bit less than 5 hours in second half. We have to weight that first. 224 km is the correct answer, 225 km is not.

The derived answer is as far as I am concerned is wrong. Because it is clearly stated that half of the journey is @21 kmph and rest is @24 kmph.

We can simply take the average speed as (21+24)/2 = 45/2.
And multiply the speed with the time taken i.e 45/2*10 = 225 km.
It is simple to derive from the distance formula i.e.

Distance = speed * time taken

Got it.

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 ?

We know that when dist traveled is equal the its harmonic mean so,

we can get by => avg speed*time= dist.

= 2(21*24)/21+24.
= 1008/45 = 22.4KM/hr.
Avg speed = 22.4km/hr.

Distance = Speed* time = 22.4*10 = 224 km.

How is @Muhammed way incorrect? that what I did it close but if this was not a multiple choice it would be wrong so can anyone explain it to me. When I mean explain like dumb it right down please.

To apply formulae 2uv/(u+v),

where,
s = Distance;
u = First Half velocity which is 21kmph
v = Second Half Velocity which is 24kmph
=>(2*21*24)/(21+24)
=>(1008)/45
=>22.4kmph.

Therefore,average speed = 22.4km/hr
s = vt
s = 22.4km/hr x 10hrs
s=224km.

Distance = (Speed x Time).

First five hours speed was 21 km/ h

So D1 = 21 * 5 = 105

Next five hours speed was 24 km / h

D2 = 24 * 5 = 120

ADD them 225 km / h which is nearer to 224 km / h

Can anyone explain me 2nd step.