MHB Distance problem. - linear equation

[paulmdrdo1]

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!

 

[Opalg]

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.

 

[paulmdrdo1]

how did you know that after 10 mins the faster runner will be two-thirds of the way round the second lap?

 

[Opalg]

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.

 

[HallsofIvy]

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.

 

[paulmdrdo1]

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."?

 

[bergausstein]

why does A have to be 1 mile more than B to overtake it? can you explain?

 

[paulmdrdo1]

that's also my question. anybody? please answer.

 

[MarkFL]

How long is one lap?

 

[paulmdrdo1]

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.

 

[MarkFL]

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

 

[paulmdrdo1]

(Dance)(Bow)(Blush) oh men! It seems I should get some rest now. To boost my critical thinking. Now I understand it clearly! Thanks!