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

Question

For the first 5 hours of a trip, a plane averaged 120 kilometers per hour. For the remainder of the trip, the plane traveled an average speed of 180 kilometers per hour. If the average speed for the entire trip was 170 kilometers per hour, how many hours long was the entire trip?

A. 15
B. 20
C. 25
D. 30
E. 35

Kudos for a correct solution.

A. 15
B. 20
C. 25
D. 30
E. 35

ynaikavde · Accepted Answer

Average speed=  \frac{TotalDistance}{TotalTime}

let the remaining time be x

total distance= 5*120+ x*180
total time= 5+x
so we have
 170=\frac{5*120+ x*180}{5+x} 
solving for x ,we get x = 25
total time 30 hours >>D

PareshGmat · Answer

Answer = D. 30

Let the distance covered  The  speed of 180 = x

Total time required  = \frac{600}{120} + \frac{x}{180} = \frac{600+x}{170}

x = 18*50*5

Total time required = 5 + \frac{18*50*5}{180}= 5 + 25 = 30

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION

lyMFLDi13C0

smashbiker84 · Answer

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.

Lucky2783 · Answer

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.

TheRzS · Answer

Tug of War Method
Let H hrs @ 170

x 5 =   x H
=>50x5 = 10xH
=>H = 25

So Total 25+5=30.  Ans D

adkikani · Answer

Bunuel   VeritasPrepKarishma   chetan2u   niks18

any alternate way to solve using  this 
blog?

niks18 · Answer

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

push12345 · Answer

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

adkikani · Answer

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.

niks18 · Answer

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

ganand · Answer

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

This can also be solved using Mixture and Alligation method.

Attachment:

Distance.png [ 3.79 KiB | Viewed 20873 times ]

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

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

Thanks.

zishu912 · Answer

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

Vsolo · Answer

Assume total time is x. Where x > 5. Then Distance covered by taking the average speed throughout x hours is equal to the sum of the distances covered at 120 Km/hr for 5 hours and 180 km/hr for (x-5) hours. We get the equation

120*5 + 180*(x-5) = 170*x

Solving for x we get 30.

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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