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

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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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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

Last edited by Carcass on 14 Mar 2018, 12:53, edited 1 time in total.
Edited by Carcass
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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!
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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?
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Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  15 Mar 2018, 02:29
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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
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Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  16 May 2018, 09:23
1
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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

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

(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

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Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  08 Jun 2018, 04:34
I still have not been able to understand why the time would taken the same for both Sue and Rob, could anybody kindly advise?
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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
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Re: Running on a 10-mile loop in the same direction, Sue ran at [#permalink]  19 Dec 2018, 09:20
1
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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

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