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

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Math Expert
Joined: 02 Sep 2009
Posts: 49960
For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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19 Feb 2015, 09:52
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Difficulty:

55% (hard)

Question Stats:

67% (02:15) correct 33% (02:40) wrong based on 290 sessions

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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.

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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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19 Feb 2015, 12:07
1
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
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For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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20 Feb 2015, 01:23
1

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 =$$5 + \frac{18*50*5}{180}= 5 + 25 = 30$$
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For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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22 Feb 2015, 12:44
Bunuel wrote:
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.

MAGOOSH OFFICIAL SOLUTION

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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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23 Feb 2015, 05:00
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.
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For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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01 Mar 2015, 23:57
1
Bunuel wrote:
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.

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

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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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11 Jan 2017, 04:23
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
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For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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21 Apr 2018, 07:59
Bunuel VeritasPrepKarishma chetan2u niks18

any alternate way to solve using this
blog?
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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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21 Apr 2018, 19:12
Bunuel VeritasPrepKarishma chetan2u niks18

any alternate way to solve using this
blog?

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
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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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21 Apr 2018, 21:36
1
Bunuel VeritasPrepKarishma chetan2u niks18

any alternate way to solve using this
blog?

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

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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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21 Apr 2018, 23:05
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.
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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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21 Apr 2018, 23:41
1
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.

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
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Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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23 Apr 2018, 05:15
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 1120 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.
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Posts: 72
Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h  [#permalink]

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23 Apr 2018, 05:38
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
Re: For the first 5 hours of a trip, a plane averaged 120 kilometers per h &nbs [#permalink] 23 Apr 2018, 05:38
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