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I travel the first part of my journey at 40 miles per hour and the

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New post 22 Jun 2019, 21:29
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I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

A. 4 hours
B. 2 hours
C. 3 hours
D. 2.5 hours
E. 5 hours

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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 23 Jun 2019, 00:59
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DisciplinedPrep wrote:
I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

A. 4 hours
B. 2 hours
C. 3 hours
D. 2.5 hours
E. 5 hours


Let the time taken for 1st part = t
—> time taken for 2nd part = 5 - t

Total distance = D1 + D2
—> 240 = 40*t + 60*(5 - t)
—> 240 = 40t + 300 - 60t
—> 240 = 300 - 20t
—> 20t = 300 - 240 = 60
—> t = 3 hours

IMO Option C

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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 23 Jun 2019, 00:42
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Hi,
The question can be done by weighted average method.
The two averages are 40 and 60 and average of entire journey is 240/5=48..
So....40...48....60.
The time for first part will be 5*(60-48)/(60-40)=5*12/20=3

C

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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 23 Jun 2019, 00:51
chetan2u wrote:
Hi,
The question can be done by weighted average method.
The two averages are 40 and 60 and average of entire journey is 240/5=48..
So....40...48....60.
The time for first part will be 5*(60-48)/(60-40)=5*12/20=3

C

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I tried to solve using allegation method
given average = 48
hence he must have covered the journey in the ratio of 3:2 for 40 kmph to 60 kmph

hence \frac{3}{5}*240 will be distance in first part
divided by avg speed of 40
gives 18/5 as time.

Where did I go wrong?
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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 13 Jan 2020, 14:59
Knowns:
Total Distance = 240
Total Time = 5

Equations:
(1) 240 = 5X (where x is the average speed)
(2) 240 = 40t1 + 60t2
(3) 5 = t1+t2

Solve for X:
X = 240/5
X = 48

Combine equations (1), (2), and (3):
5X = 40t1 + 60t2 --------------------(eq 1 and 2)
48(t1+t2) = 40t1 + 60t2 ------------(eq 3;replace 5)

Ratio method:
t1:t2
60-48:48-40
12:8
3:2

t1 = 3
t2 = 2
t1+t2 = 5
240 = 40(3) + 60(2) = 120 + 120 = 240
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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 15 Jan 2020, 14:03
From my point of view the simplest way is:

I. 60x + 40y = 240
II. x + y = 5

Which has only one solution x = 2 and y = 3 if neither x nor y are equal to 0.
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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 15 Jan 2020, 15:01
Does the wording of the question vaguely break down the journey was done in equal increments? 120 miles for the first part at 40mph and 120 miles at 60 mph for the second part?
I got the correct answer approaching it this way after faltering to find a solution using the R * T = D approach as mentioned in this thread.
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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 18 Jan 2020, 04:12
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DisciplinedPrep wrote:
I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

A. 4 hours
B. 2 hours
C. 3 hours
D. 2.5 hours
E. 5 hours


We let t = the time to complete the first part of the journey. Thus, (5 - t) = the time to complete the second part of the journey. We can create the distance equation:

40t + 60(5 - t) = 240

40t + 300 - 60t = 240

60 = 20t

3 = t

Answer: C


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Re: I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 18 Feb 2020, 20:09
DisciplinedPrep wrote:
I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

A. 4 hours
B. 2 hours
C. 3 hours
D. 2.5 hours
E. 5 hours


We can use mixtures and allegations.

Average Speed = 240/5 = 48

40 60
48
12 8

3:2

Well, we know 3 hours at 40 because 3 and 2 add up to 5.

Just to verify 3*40 + 2*60=120+120=240

Note : Even if you can't solve using this method you can just use options and work your way out.
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I travel the first part of my journey at 40 miles per hour and the  [#permalink]

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New post 18 Feb 2020, 21:37
DisciplinedPrep wrote:
I travel the first part of my journey at 40 miles per hour and the second part at 60 miles per hour and cover the total distance of 240 miles to my destination in 5 hours. How long did the first part of my journey last?

A. 4 hours
B. 2 hours
C. 3 hours
D. 2.5 hours
E. 5 hours


Use weighted averages since when averaging speed, the weights are time taken.
The two speeds are 40 mph and 60 mph and the average speed is 240/5 = 48 mph

w1/w2 = (60 - 48)/(48 = 40) = 3/2

So time taken in the first part of the journey was 3/5th of total time i.e. 3 hrs
Answer (C)

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https://www.veritasprep.com/blog/2011/0 ... -averages/
https://www.veritasprep.com/blog/2014/1 ... -averages/
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I travel the first part of my journey at 40 miles per hour and the   [#permalink] 18 Feb 2020, 21:37
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