For the first 5 hours of a trip, a plane averaged 120 kilometers per h

MAGOOSH OFFICIAL SOLUTION

we could solve it using the alligations or mixtures formula too because all the 3 avgs. namely A1 =120 , A2 = 180 and Aw = 170 are given. also n1 is given, n2 is reqd. we know that (A2-Aw)/(A1-Aw) = n1/n2..pluggin the values yield 1/5 =5/n2 or n2 =25 . total time 5 + 25 =30 hrs.

we can treat this question as a set theory question with mean of 170 .
we know that first 5 elements are 120, 120,120, 120,120 , they all lag by 50 to meet the average of 170 , in sum lag by 250 .
how many 180 should be put in order to fill this gap of 250 , if by adding one 180 we get 10 points (as the avg is 170) ? we need to add 25 180s . hence 25 hrs plane has to be driven at 180kmph so total time will be
25+5=30

thanks
Lucky

Consider +1 Kudos if you like this post.

Tug of War Method
Let H hrs @ 170

[170-120] x 5 = [180-170] x H
=>50x5 = 10xH
=>H = 25

So Total 25+5=30. Ans D

Bunuel VeritasPrepKarishma chetan2u niks18

any alternate way to solve using this
blog?

Hi adkikani

Can you explain what is your exact query here? If you are confused with the use of too many formulas, then you can always solve these type of questions using the simple concept of average speed.

Average Speed = Total Distance / Total Time &

Speed = Distance / Time

For e.g let's take the 3rd question from the blog. There are three parts to the journey and we are given speed and distance of each part. So find out the time taken to travel each part -

30 miles @ 30 miles/hr, So time taken = 30/30=1 hr

30 miles @ 60 miles/hr, So time taken = 30/60=1/2 hr

30 miles 90 miles/hr, So time taken = 30/90=1/3 hr

Total distance traveled = 30+30+30=90 miles

Total Time taken = 1+1/2+1/3=11/6 hrs

Hence Average Speed = 90/(11/6)=90*6/11=540/11

one just need to apply average speed formula

Av speed=Total distance/total time

Let total time be t
So eqn would be


170=(120*5 + 180*(t-5)) /t
Calculate t and add 5 u Will find answer

Posted from my mobile device

niks18

The OE for this is as posted by push12345 but
I wanted to reduce calculation mistakes in solving
linear equation, if possible by an alternate solution.

Hi adkikani

Ok I got your concern now. Refer to the blog whose link you had posted in your earlier post. In the blog you have below mentioned formula -

t1/t2 = (A2 – Aavg)/(Aavg – A1), now use it to calculate the missing value t2

5/t2=(180-170)/(170-120) =>t2=25

Hence total time taken = t1+t2=5+25=30

Hope this helps

Hi,
similar to the solution posted by niks18, but in diagrammatic form.

This can also be solved using Mixture and Alligation method.



T1:T2 = 10:50 = 1:5, Since T1 = 5 hrs => T2 = 5*5 = 25 hrs.

Total time = T1 + T2 = 5 + 25 = 30 hrs.

Thanks.

in first five hours plane covers 120*5 = 600kms
let say plane covered rest of the journey in t hours
so total distance covered in (5+t) hours = 600 + 180*t

Now average speed = total distance travel / total time taken

=> 170 = (600+180*t)/(5+t)
==>850 +170t = 600 + 180*t
=>250 = 10t
therefore, plane averaged 180 for the 25 hours

so total time taken = 5 + 25 = 30hours

this cant be from above 700 group questions.

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