Aptitude - Time and Distance - Discussion

9. 

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

[A]. 35.55 km/hr
[B]. 36 km/hr
[C]. 71.11 km/hr
[D]. 71 km/hr

Answer: Option C

Explanation:

Total time taken = 160 + 160 hrs. = 9 hrs.
64 80 2

Average speed = 320 x 2 km/hr = 71.11 km/hr.
9


Nisha said: (Jun 14, 2010)  
Can we use the formula for avg speed, ie: 2xy/(x+y) ?This formula gives a different answer.

S.Dineshkumar said: (Jun 16, 2010)  
Can you explain how 9/2 hrs came ...
Can you explain the question ones again?

Ranjith said: (Jun 27, 2010)  
while using the formula for avg speed, as nisha said it gives a different answer..

Sundar said: (Jun 27, 2010)  
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.

Komal said: (Jul 10, 2010)  
THANKS TO SUNDER WHO GIVES A GOOD SOLUTION

Renuka said: (Nov 9, 2010)  
Hi Sundar, very nice explaination, thank you so much.

Priya said: (Nov 29, 2010)  
@sunder Thanks.

Prveen Bilimoga said: (Dec 9, 2010)  
I have a doubt, can we do like this, the first 160 hrs is 64 km speed, and the second hr is 80, total 144. so 144/2 = to 72

Kapil said: (Dec 27, 2010)  
Since distance is same,so
avg speed= 2xy/(x+y)
avg s= (2*64*80)/(64+80)
=71.11

Jai said: (Mar 18, 2011)  
Can you explain how 9/2 hours came ?

Prajweetha said: (May 3, 2011)  
Hello jai,

By simplyfying 160/64 we will get 5/2, while 160/80 becomes 2/1
By taking 2 as LCM we will get 5+4/2=9/2

Vivek said: (Jul 23, 2011)  
Hi @Jai

5/2*2/1=by cross multiplication

We have get 5+4/2=9/2

S. M. said: (Aug 2, 2011)  
Simple method :- (64+84)/2 =72

Thus on safer side,

we can go with C.) 71.11 km/hr

Sugumaran said: (Aug 8, 2011)  
Hai praveen and S. M.

Your method is not suitable for all cases. Please avoid this method for solving this type of questions.

Fatima said: (Oct 18, 2011)  
Thank you so much Sundar.

Shro said: (Feb 19, 2012)  
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)

Samy said: (Mar 1, 2012)  
Thank you suguraman.

Anshu said: (Mar 13, 2012)  
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........

Samiksha said: (Aug 25, 2012)  
Simply you can aplly the formula ie,

2ab/a+b

then, you will get your answer.

Siva said: (Oct 19, 2012)  
Speed=distance/time.

A) first time: 160/64 = 2.5.

B) second time: 160/80 = 2.

a+b = 2. 5+2 = 4.5.

Average speed=320/4.5 = 71.11.

Jeevan said: (Apr 3, 2014)  
We have to use like this also,

Total distance = 320.
1st half = 160.
2nd half = 160.
1st half speed = 64km/hr.
2nd half speed = 80km/hr.

Avg speed of 320km(dist) = 2*(64*80)/64+80 = 71.11 km/hr.

Javid Mir said: (Aug 6, 2014)  
Simple;

Average speed = 2xV1xV2/V1+V2.
Avg. Speed = 2x64x80/64+80.
Avg. Speed = 2x64x80/144.
Solving we get; avg speed = 71.1 Km/hr.

Sajnan said: (Sep 2, 2014)  
This is simple:

First calculate 160/64 = 2.5.
Then 160/60 = 2.

=>2.5+2 = 4.5.

Then calculate 320/4.5 = 71.11.

Damodhar said: (Apr 29, 2015)  
Average speed = (2*80*64)/(64+80) = 71.11.

Laxmi said: (Mar 1, 2016)  
Excellent way of clarifying the doubts.

Vengatesh said: (Apr 4, 2016)  
Super, Thank you all.

Roksana1 said: (Jun 2, 2016)  
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.

Rahul said: (Sep 3, 2016)  
Why can't we use 64 + 80/2 = 72?

Gayathri said: (Sep 4, 2016)  
@Sundar. Your explanations always make me clear, Thanks.

Swapnil said: (Feb 6, 2017)  
(64+80)/2 = 72.

This answer aprox to 71.11
Therefore the answer is 71.11.

Jitender Yaggik said: (Jun 2, 2017)  
@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.

Shivani said: (Oct 4, 2017)  
Sir, it is asking for 320 km so how can we apply this formula 2xy/ (x+y)?

Ajay said: (Jan 8, 2018)  
Total speed 320km/hr.

64km/h + 80km/hr= 144km/hr.
So the average speed is 144/2= 72 km/hr.

Prashanthi said: (Jun 29, 2018)  
Thanks for the solution @Kapil.

Arjun said: (Jul 14, 2018)  
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.

Pronoi said: (Jul 18, 2018)  
Average speed =2 * 64 * 80/64+80.
= 10240/144.
= 71.11 km/hr.

Tridib Samanta said: (Jul 28, 2018)  
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!

Priyadharshini G. said: (Aug 10, 2018)  
Given,

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

Here the distance are same.
Avg. speed = 2 x y /(x+y).
=2 * 64*80/(64+80).
=71.11 km/hr.

Rahul said: (Sep 7, 2018)  
@Sundar.

It's so difficult to cut 10240/144.

Muklesur said: (Sep 29, 2018)  
2xy/x+y.

2*64*80/64 + 80.
71.111 km/h.

Divya said: (Oct 7, 2018)  
Good, Thanks @Sundar.

Kartik said: (Oct 9, 2018)  
A car travelled 80km/h. What should be its speed for next 4h, so that the total average speed become 14km/h?

Can anyone answer this with the explanation?

Sushil said: (Oct 25, 2018)  
Thanks alot for the answer @Sundar.

Kiran said: (Nov 18, 2018)  
Thanks, @Sundar.

Girish said: (Dec 26, 2018)  
Well explanation, Thanks.

Aryan said: (Jan 27, 2019)  
How did 9/2 came? please explain me.

Akshay Patel said: (Jul 9, 2019)  
Avg speed of x and y be x+y/2.

Then given that 64+80/2=72.

Ravi said: (Jul 21, 2019)  
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.

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