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

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Question Stats:

78% (01:16) correct
21% (01:31) wrong based on 38 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

3

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
_________________

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

2

This post received KUDOS

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:

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

1

This post received KUDOS

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: 8t = 6t + 10 Solve to get: t = 5

Answer: C

RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
19 Dec 2018, 09:11

Expert's post

Shrija Roy wrote:

I still have not been able to understand why the time would taken the same for both Sue and Rob, could anybody kindly advise?

They both started running at the same time, and we stopped the clock (for both runners) once Sue lapped Rob.

Cheers, Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]
19 Dec 2018, 09:20

1

This post received KUDOS

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

As I mention in the video below, we can often solve these kinds of problems using more than 1 approach. So, instead of comparing distances (as I did above), let's compare times

Our word equation can be: Sue's travel time = Rob's travel time

Let x = the distance Rob traveled We know that Sue traveled ONE LAP more than Rob traveled. Since 1 lap = 10 miles, we know that Sue traveled 10 miles MORE THAN Rob. This means x + 10 = the distance Sue traveled

time = distance/speed So, our word equation becomes: (x + 10)/8 = x/6 Cross multiply to get: 6(x + 10) = 8(x) Expand to get: 6x + 60 = 8x We get: 60 = 2x So, x = 30

This means ROB traveled 30 miles (and it means SUE traveled 40 miles)

If they began running at the same point on the loop, how many hours later did Sue complete exactly 1 more lap than Rob? time = distance/speed Let's use Rob's distance and speed to get: time = 30/6 = 5 hours

Answer: C

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

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Re: Running on a 10-mile loop in the same direction, Sue ran at
[#permalink]
19 Dec 2018, 09:20