Aptitude - Time and Distance - Discussion

There said half the journey. So why didn't we get half the time for calculation.

Like (5*24)+(5*21) = 225.

Simple trick.

Find average speed because they are given half and half journey.

2xy/x+y......> 2(21)(24)/(21+24).

So average speed = 2(21)(24)/45.

Therefore D = S*T.

= [2(21)(24)/45]*10 = 224.

Average speed = (2*21*24)/(21+24) = 102/5.

Distance = (102*10)/5 = 224.

Following is explanation:

Total Travel Time = 10 hours.

Let's assume Total Distance = d kms and 1st half (i.e d/2) was completed in x hours at speed of 21 kmph.

=> d/2 = 21x.

=> d/42 = x.....equation (1).

=> 2nd half (i.e d/2) was completed in (10-x) hours @ speed of 24 kmph.

=> d/2 = 24*(10-x).
=> d/48 = 10-x.

=> x = 10-(d/48)....equation (2).

From equation (1) and (2),

=> d/42 = 10-(d/48).
=> d/42 + d/48 = 10.
=> d = 2*5*2*3*7*8/(3*5).
=> d = 224 kms.

First half of journey means half distance of journey. Not half ours of time. May it will help you.

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

Where,

s = Distance;

u = First Half velocity which is 21 kmph.

v = Second Half Velocity which is 24 kmph.

=> (2*21*24)/(21+24).

=> (1008)/45.

=>22.4 kmph.

Therefore, average speed = 22.4 km/hr.

s = vt.
s = 22.4 km/hr x 10hrs.
s = 224 km.

I ll tell you people the easiest method.

Average speed = 2xy/(x+y) = 22.4.

Time is given 10 hrs.

So 10x22.4 = 224.

How does 15x arrived?

Here you need to know first that average speed is the uniform speed.

That is if the person travelled with the uniform speed then he would complete the journey in 10 hrs and cover the given distance as well. We don't know the distance and we are given two different speeds for half the journey.

Now as we can see the last formula in the important formula section for this chapter. We can get the average speed as: 2xy/(x+y).

So average speed = 2x21x24/(21+24).

Now not getting the exact average speed I reduce the above by basic division as.

Average speed = (2x7x8)/5.

But Distance = Speed*Time.

So, D = [(2x7x8)/5]*10 (Now 10/5 is 2 so the equation becomes).

2*7*8*2 = 224 km that's it!

First half of the journey is 21 km, 24 km.

Average speed during 21 km, 24 km = 2xy/x+y.

= 2 (21*24) /21+24.

= 1008/45 = 112/5.

He complete the hole journey in 10 hrs.

So, 112/5*10 = 224.

Thank you!