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Davis drove from Amityville to Beteltown at 50 miles per hour, and ret

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Bunuel
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Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   Updated on: 12 Jul 2021, 06:11
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Davis drove from Amityville to Beteltown at 50 miles per hour, and returned by the same route at 60 miles per hour. What was Davis’ average speed for the round trip, in miles per hour ?

A. 53
B. 54
C. 600/11
D. 55
E. 56
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C

Originally posted by Bunuel on 12 Jul 2021, 04:15.
Last edited by chetan2u on 12 Jul 2021, 06:11, edited 1 time in total.
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   12 Jul 2021, 04:58
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Solution:

We will assume the distance between Amityville to Beteltown be \(D\) miles.

So, time taken to go from Amityville to Beteltown \(= \frac{D}{50}\) hours (\(Time = \frac{Distance}{Time}\))

And time taken to go from Beteltown to Amityville \(= \frac{D}{60}\) hours (\(Time = \frac{Distance}{Time}\))

So total time of the journey \(= \frac{D}{50} + \frac{D}{60} = \frac{(6D+5D)}{300} = \frac{11D}{300}\)

Total distance of the journey \(= D + D = 2D\)

Average Speed \(= \frac{Total Distance }{ Total Time} = \frac{2D}{11D/300} = \frac{600}{11}\)

Hence the right answer is Option C.
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   14 Jul 2021, 06:24
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Since, the distance is same , average speed is harmonic average = \(\frac{2 * 50 * 60 }{ (50 + 60)} = \frac{2 * 50 * 60 }{ 110} = \frac{600}{11}\)

Answer C
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   12 Jul 2021, 04:22
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We can just imagine the distance one-way is 300 miles. Then he spends 6 hours one way and 5 hours the other, and drives 600 miles in total, so his average speed is 600/11 miles per hour.
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   14 Jul 2021, 04:33
Average speed when Distance is constant = 2ab/a+b

a= 50mph
b= 60mph

Average speed = (2*50*60)/(50+60)

= (2 *50*60)/110
=600/11

Answer option C
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink] New post   17 Feb 2023, 05:57
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Re: Davis drove from Amityville to Beteltown at 50 miles per hour, and ret [#permalink]
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