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GRE Math Challenge #7-David drove to work at an average

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GRE Math Challenge #7-David drove to work at an average [#permalink] New post 15 Sep 2014, 22:03
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Question Stats:

59% (00:40) correct 40% (00:28) wrong based on 69 sessions
David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A)48
B)\(\frac{256}{5}\)
C)\(\frac{360}{7}\)
D)\(\frac{105}{2}\)
E)\(\frac{160}{3}\)
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 27 Jan 2018, 21:36
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 02 Feb 2018, 08:55
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The total distance going from home to work = total distance going from work to home
In the 1st case David drove @ an average speed of 45 miles per hour so distance \(d = 45 h1\)where \(h1\)is the time taken to complete the distance
In the 2nd case David drove @ an average speed of 60 miles per hour so distance \(d = 60 h2\)where \(h2\)is the time taken to complete the return journey from work to home
Given,
\(h1 + h2 = 2\)
we get,\(h1 = 2 - h2\)
Since distance is equal for going to work from home and coming back to home from work
\(45h1 = 60h2\)
hence, \(45(2 - h2) = 60 h2\)
solve for h2 it should equal\(\frac{90}{105}\)
Solve for D by replacing value of h2 in the eqn \(60* h2\)
\(d =\frac{360}{7}\)
(C)
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 03 Feb 2018, 04:10
Great Job!!!
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 03 Feb 2018, 07:55
C : 360/7
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 25 Feb 2018, 05:35
From home to work: 45 = t1*d
From work to home: 60 = t2*d

The distance d is the same for both trips, and also t1 + t2 = 2

So t1 = d/45 and t2 = d/60.

Substitute away t1 and t2 in the total time equation: d/45 + d/60 = 2.

Now solving for d: (60d + 45d)/2700 = 2 --> 105*d = 5,400 --> d = 360/7.
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 11 Apr 2018, 21:36
speed = distance/ time

We will get 2 equation for 1. To office and 2. Back from office.

Solving for 2 variables from 2 equations gives the answer.
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Re: GRE Math Challenge #7-David drove to work at an average [#permalink] New post 03 Sep 2018, 17:54
the equation is x/45 + x/60 = 2 ==> x = 360/7

where X is the distance between home and office.
Answer -option C
Re: GRE Math Challenge #7-David drove to work at an average   [#permalink] 03 Sep 2018, 17:54
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GRE Math Challenge #7-David drove to work at an average

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