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Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
13 Mar 2018, 09:06

00:00

Question Stats:

76% (01:04) correct
23% (01:43) wrong based on 13 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?

Re: Question on work/rates - please help! [#permalink]
14 Mar 2018, 01:25

1

This post received KUDOS

Expert's post

Shrija Roy wrote:

2. 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

Rewriting the question: How many hours later was Sue 10 miles ahead of Rob.

Say this happens x hours later.

So; distance covered by Sue in x hours -distance covered by Rob in x hours = 10 miles

or \(8 \times x - 6 \times x =10\). Solving for x; \(x=5\) hours.

Hence option C is correct! _________________

Sandy If you found this post useful, please let me know by pressing the Kudos Button

Re: Question on work/rates - please help! [#permalink]
14 Mar 2018, 07:29

Sorry, one question here -

Sue has a speed of 8m/hr and Rob has the speed of 6 m/hr. So how are we taking the same x time? Ideally, speed is inversely proportional to time so Sue should complete the lap early, no?

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
15 Mar 2018, 02:29

2

This post received KUDOS

For every hour sue has a lead of \(\frac{2miles}{hr}\) over Rob. To get an exact 1 lap lead sue has to have total lead of \(10\) miles as the lap is 10 miles long Hence \(\frac{10}{2} = 5\). Time that is required to put a one lap lead on Rob option c
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
16 May 2018, 09:23

Expert's post

Shrija Roy wrote:

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

When Sue completes exactly 1 more lap than Rob, she will have traveled exactly 10 miles more than Rob (since the loop is 10 miles long). We can let both of the times = t and create the equation:

8t = 6t + 10

2t = 10

t = 5

Answer: C
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GRE Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
16 May 2018, 10:10

Expert's post

Shrija Roy wrote:

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

1 lap = 10 miles So, if Sue completes 1 lap more than Rob completes, then we know that Sue has traveled 10 miles more than Rob

So, let's start with a word equation: (Sue's travel distance) = (Rob's travel distance) + 10 miles

Distance = (speed)(time) We know each person's speed, but we don't know their travel times. Let t = Sue's travel time So, t = Rob's travel time also

Now take our word equation and plug in the necessary values: 10t = 8t + 10 Solve to get: t = 5

Answer: C

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