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

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Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
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Solution

Given:
• Sue and Ron are running on a 10-mile loop in the same direction
• Sue ran at a constant rate of 8 mph
• Rob ran at a constant rate of 6 mph
• They began running at the same point on the loop

To find:
• In how many hours Sue completed exactly 1 more lap than Rob

Approach and Working:

• Sue ran at 8 mph and Rob ran at 6 mph
o Therefore, in every hour, Sue created a gap of 2 miles between them

• If Sue completed exactly 1 more lap than Rob, it effectively means Sue created a gap of 10 miles between her and Rob (as the loop distance is 10 miles)
• Now, if 2 miles of gap was created in 1 hour, 10 miles of gap was created in $$\frac{10}{2}$$ hrs = 5 hrs

Hence, the correct answer is option C.

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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
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Bunuel 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 a constant [#permalink]
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Bunuel 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 a constant [#permalink]
EgmatQuantExpert wrote:

Solution

Given:
• Sue and Ron are running on a 10-mile loop in the same direction
• Sue ran at a constant rate of 8 mph
• Rob ran at a constant rate of 6 mph
• They began running at the same point on the loop

To find:
• In how many hours Sue completed exactly 1 more lap than Rob

Approach and Working:

• Sue ran at 8 mph and Rob ran at 6 mph
o Therefore, in every hour, Sue created a gap of 2 miles between them

• If Sue completed exactly 1 more lap than Rob, it effectively means Sue created a gap of 10 miles between her and Rob (as the loop distance is 10 miles)
• Now, if 2 miles of gap was created in 1 hour, 10 miles of gap was created in $$\frac{10}{2}$$ hrs = 5 hrs

Hence, the correct answer is option C.

I think this can also be solved using the LCM approach as follows:

At his constant rate of 8 mph, Sue can complete 10 miles in 10/8 hours or 75 minutes
Likewise, at his constant rate of 6 mph, Rob can complete 10 miles in 10/6 hours or 100 minutes.
At the time that Sue would have completed, exactly 1 more lap than Rob, both of them will meet at the starting point for the first time. So the question can be rephrased to: "How long will it take for both of them to meet at the starting point for the first time?"
This question can be answered by simply taking the LCM of 100 and 75.
LCM (100, 75) = 300.
So it will take 300 minutes for both of them to meet at the starting point for the first time. 300 minutes is equal to 5 hours (300/60). So the correct answer is C.
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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
Bunuel, is there a mistake in the question 'how many hours later did Sue complete exactly 1 more lap than Rob?' ? shouldn't it be Rob complete 1 more lap than Sue since her speed is greater ? or am i interpreting the question wrong.
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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
Approach:

- Both Sue and Rob started at same point and time, with speed 8 miles per hour and 6 miles per hour

- After 1 hr, distance between both is 2 miles. OR for 2 miles difference -> 1 hr

Hence,
- for 10 miles (1 loop) difference -> 5 hrs

Option C
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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
Top Contributor
Bunuel 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 gap

Distance gap between them:

$$8x-6x=10$$

$$2x=10$$

$$x=5$$

The answer is $$C$$
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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
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Re: Running on a 10-mile loop in the same direction, Sue ran at a constant [#permalink]
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