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In a 40-mile trip, the first 20 miles were traveled in 50mph. If the t

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In a 40-mile trip, the first 20 miles were traveled in 50mph. If the t  [#permalink]

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New post 15 Jul 2015, 19:10
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Question Stats:

88% (01:52) correct 12% (03:02) wrong based on 60 sessions

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In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40



This question dos not apear to be difficult, but it took me too much time to solve. Does anyone has a fast way of killing it?
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Re: In a 40-mile trip, the first 20 miles were traveled in 50mph. If the t  [#permalink]

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New post 15 Jul 2015, 19:18
Mascarfi wrote:
In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40



This question dos not apear to be difficult, but it took me too much time to solve. Does anyone has a fast way of killing it?


Do not change the wording of the question. The same question has been discussed at the location : a-driver-completed-the-first-20-miles-of-a-40-miles-trip-at-130648.html?fl=similar . Please search the forums before you post a new question.

As far as your question is concerned, the simplest way is to observe that the distance of 20 miles is half of 40 miles. Thus treating this as a simple average problem , we can see that for 2 things to have an average of 60 with 1 being 50, the other needs to be just more than 60 to bring the average up to 60. Thus B is the only logical answer. Option A will give you a comparatively higher average value while rest of the options will decrease the average.

The above method was applicable only because the speeds given were exactly at mid way of the total distance. Had it been at any other point (2/3rds of the total distance etc) then we would have to apply the average speed formula.
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In a 40-mile trip, the first 20 miles were traveled in 50mph. If the t  [#permalink]

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New post 15 Jul 2015, 20:33
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Mascarfi wrote:
In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40



This question dos not apear to be difficult, but it took me too much time to solve. Does anyone has a fast way of killing it?


METHOD-1

Time = Distance / Speed

Time to travel First 20 miles = 20/50 = 2/5 hours

Total Time to cover 40 miles = 40/60 = 2/3 hours

i.e. Time to cover last 20 miles = (2/3)-(2/5) = 4/15 hours

Speed = Distance / Time

Speed while covering last 20 miles = 20/(4/15) = 75

METHOD-2

Average speed for equal to and fro motion = 2ab / (a+b) where a and b are speeds in to and fro cases

60 = 2*50*b/(50+b)

i.e. b = 75

Answer: Option B
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In a 40-mile trip, the first 20 miles were traveled in 50mph. If the t   [#permalink] 15 Jul 2015, 20:33
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