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.

First 160 km: Speed is 64 kmph.
Second 160 km:- Speed is 80 kmph.

So, just use Average speed = (2xy)/x+y = (2*64*80)/64+80 = 71.11 kmph.

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.

The average speed = 2xy/(x+y).
where x=64 kmph y = 80 kmph,
Therefore, 2(64)(80)/(64+80) = (8)(80)/9.
= 640/9.
= 71.11 kmph.

At 64 km/hr it will take 2.5 hrs for travelling 1st 160 km and at 80 km/hr it will take 2 hrs for travelling 2nd 160 km.

So, the total 4.5 hrs for 320 km.
So 320 / 4.5 === 71.11 km Average speed.

Why can't we use 64 + 80/2 = 72?

Thanks for the solution @Kapil.

Sir, it is asking for 320 km so how can we apply this formula 2xy/ (x+y)?

Why can't we just take the average of the two numbers and divide by 2, since distance travelled at both the speeds is same.

We get the answer as 72.

Average speed =2 * 64 * 80/64+80.
= 10240/144.
= 71.11 km/hr.