Aptitude - Time and Distance - Discussion

To find the average speed for the first 320 km of the tour, we can use the formula for average speed, which is the total distance traveled divided by the total time taken.

Given:

Distance 1 = 160 km
Speed 1 = 64 km/hr
Distance 2 = 160 km
Speed 2 = 80 km/hr.

We can calculate the total time taken for the first 320 km as follows: Time taken for the first 160 km = Distance 1/Speed 1 Time taken for the next 160 km = Distance 2/Speed 2.

Total time taken = Time taken for the first 160 km + Time taken for the next 160 km.

Total time taken = (Distance 1/Speed 1) + (Distance 2/ Speed 2)
Total time taken = (160/64) + (160/80).

Now, we can find the average speed: Average speed = Total distance / Total time taken Average speed = (Distance 1 + Distance 2)/Total time taken Average speed = 320/ ((160/64) + (160/80)).

By evaluating the expression, we can find the average speed for the first 320 km of the tour.

Hi Nisha and Ranjith,



Average speed = 2xy/(x+y)



Where x = 64 km/hr and y = 80 km/hr.



Avg Speed = (2 x 64 x 80)/(64 + 80)



= 10240/144



= 71.111 km/hr



It is giving the correct answer only. Please make sure once again.





Hi Dinesh,



Your doubt is "How did 9/2 hrs come?".



1. The time taken for travelling first 160 km at 64 km/hr is = 160/64 = 2.5 hrs.



2. The time taken for travelling the next 160 km at 80 km/hr is = 160/80 = 2 hrs.



Therefore, total time taken (for 160 + 160 = 320 km) = 2.5 + 2 = 4.5 hrs.



We can write 4.5 hrs as 9/2 hrs. <-- I hope this is what you expect.





Now finding the avg speed.



1. Total distance = 320 km.



2. Total time taken = 4.5 hrs.



Avg Speed = 320/4.5 = 71.11111... km/hr



Note: Both methods are giving the same answer.

As the distance of the first half and the second half of the journey is same, i.e. 160 kms.
We can use the formula - [ 2xy / x+y],
=> (2x64x80) / (64+80),
=> 10,240 / 144,
=> 71.1111 km/hr.

Which gives the average speed for the entire journey!

Please note that you could use this formula ONLY IF distances of both halves are SAME.
Here in this problem 160 km each half. So, 320 km total distance of the journey.
All the best!

I'm using solution in this way. Whether it is correct way let me know.

Distance 1 = 160km.
Speed 1 = 64km/hr.

Distance 2 = 160km.
Speed 2 = 80km/hr.

If average distance is 320km.

Then let assume Avg speed = x.

So,

160/64 + 160/80 = 320/x.

20/8 + 16/8 = 320/x (to make the calculation easy let shortleft handed => 20 + 16/8= 320/x numbers).

=> 36/8 = 320/x.

x = 2560/36.
x = 71.11km/hr.

@ALL.

Some of my friends are confused in Speed formulas some are using a+b/2 and some are using 2ab/a+b. Now I am going to clear that point, first of all when the distance is same In both then we will use the second formula which is Harmonic mean (2ab/a+b) and when the time is same in both cases then we will use Arithmetic mean a+b/2.

Thank you.

Formula use to average speed is 2xy/x+y.
First speed is x = 64,
Second speed is y = 80.
Put the speeds values in the formula.
= 2xy/x+y.
= 2x64x80/64+80,
= 10240/144,
= 71.1111 km/hr ans.

For the first 160km time taken is t = d/s t = 160/64 = 2.5hr,
For the second 160km, the time taken is t=d/s t=160/80 = 2hr.
Average speed = total distance/total time taken.
= 160+160/2.5+2.
= 320/4.5.
= 71.11 km/hr.

Time = distance speed^-1
time = 160 / 64 = 10 / 4 = 2.5 hour
time taken for the second half = 160 / 80 = 2 hour
total time taken = 4.5 hour
total distance = 160 + 160 = 320
speed = distance time^-1
speed = 320 / 4.5 = 3200/ 45 = 355.5555.../5 = 71.1111........

For 1st 160km time taken will be =160/64 = 2.5 sec.
For 2nd 160km time taken will be = 160/80 = 2 sec.

Total time taken in journey = 2.5 + 2 = 4.5 sec.

The avg speed for 320 km will be=total distance travelled/total time.
So,, 320/4.5 = 71.11 kmph.

Guys,Why ru making it so comlicated...its simple speed=distance by time formula.
then distance is 320 and time is 9/2.
So speed=(320)/(9/2)
which is as per simple calculation
it can also be written as:
320*(2/9)