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# Running on a 10-mile loop in the same direction, Sue ran at

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  14 Jun 2018, 14:39
Expert's post
00:00

Question Stats:

70% (00:45) correct 29% (00:09) wrong based on 17 sessions
Running on a 10-mile loop in the same direction, Sue ran at a constant rate of 8 miles per hour and Rob ran at a constant rate of 6 miles per hour. If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1734 [0], given: 397

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  07 Jul 2018, 04:28
Expert's post
Explanation

If Sue completed exactly one more lap than Rob, she ran 10 more miles than Rob. If Rob ran d miles, then Sue ran d + 10 miles. Rob and Sue began running at the same time, so they ran for the same amount of time. Let t represent the time they spent running. Fill out a chart for Rob and Sue, using the formula Distance = Rate × Time (D = RT):

 D(miles) = R(miles per hour) $$\times$$ T (hours) Rob d = 6 $$\times$$ t Sue d+10 = 8 $$\times$$ t

There are two equations:

$$d = 6t d + 10 = 8t$$

Substitute 6t for d in the second equation and then solve for t:

$$6t + 10 = 8t$$

$$10 = 2t$$

$$5 = t$$

Hence option C is correct!
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Sandy
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Intern
Joined: 27 Oct 2018
Posts: 49
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Kudos [?]: 12 [0], given: 27

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  04 Nov 2018, 08:11
Difference in distance/Difference in speeds = 10/(8-6) = 5
Re: Running on a 10-mile loop in the same direction, Sue ran at   [#permalink] 04 Nov 2018, 08:11
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