Distance problem. - linear equation

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Discussion Overview

The discussion revolves around a distance problem involving two runners, A and B, who run around a circular mile track at different speeds. Participants explore how long it will take for them to pass each other when running in the same direction and in opposite directions. The scope includes mathematical reasoning and conceptual clarification of the scenario.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that A runs at 1/6 mile per minute and B at 1/10 mile per minute, calculating A's relative speed to B as 1/15 mile per minute.
  • Another participant questions how the conclusion about the faster runner being two-thirds of the way around the second lap after 10 minutes was reached.
  • Some participants express confusion about the concept of A needing to run one mile more than B to overtake him.
  • One participant clarifies that since the track is one mile long, when the faster runner laps the slower runner, he has run exactly one mile more.
  • Another participant reiterates the difficulty in picturing the scenario clearly, indicating a need for further explanation.

Areas of Agreement / Disagreement

Participants generally agree on the calculations for the second part of the problem but express uncertainty and confusion regarding the first part, particularly about the overtaking concept and how to visualize the scenario. No consensus is reached on the explanation of the first question.

Contextual Notes

Some participants struggle with the visualization of the problem and the underlying assumptions about relative speeds and distances. The discussion reflects varying levels of understanding and interpretation of the problem.

Who May Find This Useful

Individuals interested in distance problems, mathematical reasoning, and conceptual understanding of relative motion in physics may find this discussion beneficial.

paulmdrdo1
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A and B can run around a circular mile track in 6 and 10 minutes respectively. If they start at the same instant from the same place, in how many minutes will they pass each other if they run around the track (a) in the same direction, (6) in opposite directions?

I know how to solve b my answer is 3.75 mins.

but I don't get the first question. I can't clearly picture the scenario in my mind for the 1st question. can you provide an explanation for it. thanks!
 
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For (a), think about what happens after 10 minutes. At that point, the slow runner will have completed one lap, but the faster runner will already be two-thirds of the way round the second lap, and before long will overtake the slower runner. It's that overtaking moment that you are looking for.
 
how did you know that after 10 mins the faster runner will be two-thirds of the way round the second lap?
 
paulmdrdo said:
how did you know that after 10 mins the faster runner will be two-thirds of the way round the second lap?
Because he/she will have completed the first lap in 6 minutes and will then have had another 4 minutes, in which time s/he will have completed 4/6 of a lap.
 
paulmdrdo said:
A and B can run around a circular mile track in 6 and 10 minutes respectively. If they start at the same instant from the same place, in how many minutes will they pass each other if they run around the track (a) in the same direction, (6) in opposite directions?

I know how to solve b my answer is 3.75 mins.

but I don't get the first question. I can't clearly picture the scenario in my mind for the 1st question. can you provide an explanation for it. thanks!
Here's how I would do it. Since the track is one mile long, A is running at 1/6 mile per minute and B is running at 1/10 mile per minute. A's speed, relative to B is 1/6- 1/10= 5/30- 3/30= 2/30= 1/15 mile per minute. To pass B, A must have run one mile more than B in the same time. At 1/15 mile per minute, it would take A 15 minutes to do that.

When they run in opposite directions, so they are "closing" on each other, their relative speeds are 1/6+ 1/10= 5/30+ 3/30= 8/30= 4/15 mile per minute. To go one mile at 4/15 mile per minute would require 15/4= 3.75 minutes as you say.
 
what do you mean by "A's speed, relative to B is 1/6- 1/10= 5/30- 3/30= 2/30= 1/15 mile per minute."?
 
Last edited:
why does A have to be 1 mile more than B to overtake it? can you explain?
 
that's also my question. anybody? please answer.
 
How long is one lap?
 
  • #10
the circular lap is one mile. It still can't picture it clearly. this is one of the problems that always get me scratching my head.
 
  • #11
Okay, since the lap is one mile long, then when the faster runner laps the slower, he/she has then run exactly one mile more. :D
 
  • #12
(Dance)(Bow)(Blush) oh men! It seems I should get some rest now. To boost my critical thinking. Now I understand it clearly! Thanks!
 

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