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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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15 May 2018, 01:28
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Difficulty:

25% (medium)

Question Stats:

76% (01:17) correct 24% (01:53) wrong based on 126 sessions

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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

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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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15 May 2018, 02:35
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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

Relative distance needed = 1 loop - 10 miles

Relative Speed = 8-6 = 2 miles per hours (Relative speed is the change of distance between two objects in Unit Time)

Time taken to cover the relative distance @ Relative Speed = Distance / Speed = 10 / 2 = 5 Hours

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

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15 May 2018, 05:05
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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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15 May 2018, 06:31
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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
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 a constant  [#permalink]

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16 May 2018, 09:53
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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19 Dec 2018, 13:51
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

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 &nbs [#permalink] 19 Dec 2018, 13:51
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