Aptitude - Time and Distance - Discussion

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!

First half journey is 21 km/hr and 2 and half is 24 km/hr.

So we can calculate as 21*10 = 210 and divide as half by 2 is 105 same as it as for 24 km 24*10 = 240 and divide as half = 120.

So 120+110 = 225.

Then how is 224? Is this logic is also correct?

We should not take average speed, in this case, it is clearly mentioned that 1st half and 2nd half.

Thank you so much @Sakthivel.

Please explain the first line of the solution.

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.

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.

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

[ ................................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.