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Running on a 10-mile loop in the same direction, Sue ran at
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Updated on: 14 Mar 2018, 12:53
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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?
Re: Question on work/rates - please help!
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14 Mar 2018, 01:25
3
Expert Reply
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!
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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
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15 Mar 2018, 02:29
2
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
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16 May 2018, 09:23
2
Expert Reply
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:
Running on a 10-mile loop in the same direction, Sue ran at
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16 May 2018, 10:10
2
Expert Reply
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
Re: Running on a 10-mile loop in the same direction, Sue ran at
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19 Dec 2018, 09:20
1
Expert Reply
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
Re: Running on a 10-mile loop in the same direction, Sue ran at
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07 Jun 2021, 01:59
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