Questions on Circular Tracks and RTD

[shubha2110]

For the problems on circular track and RTD, what are the basic concepts and variations possible? How important are these from the pt of view of the gmat? Got a question on circular tracks in MGMAT4 as below. Need more explanation and hints on how to solve these kind of problems 'quickly'.

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?

4pi- 1.6
4pi+ 8.4
4pi+ 10.4
2pi- 1.6
2pi- 0.8

Also, 2 more questions:
1. What degree of understanding of clocks - time of meeting, angle between hands etc is necessary for gmat?

2. I am able to solve most of the quant questions on my own post the test but during the test, I just don't. Have found that I am not quick enough and have to guess on over 12 ques to complete the test on time.

For example, on an inequalities q, so many permutations to try or in a word problem, its long and complex. What can I do to build speed without compromising my accuracy? Taken 4 tests; started with 690 -> 700 -> 720 -> 700. Its not moving above 720 with quant at 70 to 74%ile.

Hope you can help.
Thanks
Subhashini

[tim]

Circular tracks are no different from other RTD questions aside from the repetitive nature of the course. So all the typical RTD question variations could show up on questions about circular tracks as well, and the techniques you use on ordinary RTD questions will work on circular track questions as well..

Angle between hands questions are probably not going to become an issue on the GMAT, and to the extent that they do you’re probably okay as long as you remember that the hour hand will take one hour to go between two numbers, the minute hand takes an hour to go a full 360 degrees, and there are 12 numbers on the clock. Everything else is derivable from there..

The answer to your second question is practice and THOROUGH review. You need to ask yourself why you weren’t able to solve a question on the test but you could later. Ask yourself what type of problem it was and how you could have recognized what strategy to use. Ask yourself where things went wrong. If you can answer these questions, you’ll be well on your way to figuring out why you’re having this trouble and being able to fix it..

[dw6586]

can you please explain how to get to the answer in this question? the issue i'm having is when they meet. how do i calculate the moment they pass each other? i get really confused at these track questions when they have this element of crossing paths... thanks

[tim]

tell us a little about what you did and where it went wrong, and we'll be able to help you further..

[dw6586]

i was able to make a R*T=D chart for A and B separately, but then i couldn't figure out how to calculate the moment they passed each other and fill in a chart to find the time they're asking for.

[tim]

sounds like you're on the right track. show us your chart and i think we'll be able to point you in the right direction..

[AbigailS228]

I have a similar problem with this question. I understand that when A starts, Car B has gone 20pi-20. What I don't understand about the explanation given is where the 8 came from: 12 miles: (20 – 20) + 12 = (20 – 8) miles.

I made the RTD chart and got
5t=?

Then I get stuck. Please help!

[RonPurewal]

I have a similar problem with this question. I understand that when A starts, Car B has gone 20pi-20. What I don't understand about the explanation given is where the 8 came from: 12 miles: (20 – 20) + 12 = (20 – 8) miles.

I made the RTD chart and got
5t=?

Then I get stuck. Please help!

Seems there are some characters missing from your post. E.g., "20 – 20" would just be zero, which, in context, is obviously not what you mean.

In any case, here's a summary:
• The entire distance around the circle is 20pi.
• In the time during which car B is traveling alone, it travels 20 miles.
• Let's look only at the situation after that time, so that both cars travel for the same amount of time.

To meet each other, the cars need to travel the rest of the circle's circumference. That's 20pi (the whole circumference) minus 20 (the distance that car B has already covered.). So, "20pi – 20" is the distance that the cars must cover (together) to meet again.

But, we don't just want them to meet again; we want them to travel 12 more miles after that. So, we want them to travel a total distance of (20pi – 20) + 12, or 20pi – 8 miles.

[AbigailS228]

Of course! So then do you solve for t (hours) and then add 10 since we are looking for the time of Car B (who's already traveled 10 hours)?

Thanks so much! Stupid question in hindsight.

[RonPurewal]

Of course! So then do you solve for t (hours) and then add 10 since we are looking for the time of Car B (who's already traveled 10 hours)?

Yes.

[RonPurewal]

Stupid question in hindsight.

In that case, it's the hindsight that's "stupid", rather than the question.

(:

Don't deprecate the learning process.

[SubhajitS796]

Is the answer to the first question is 4pi -1.6??

[RonPurewal]

Is the answer to the first question is 4pi -1.6??

nope.
better check your "a"s and "b"s

[RonPurewal]

(i.e., you've found the right kind of answer, but for the wrong car.)

[RonPurewal]

by the way, i'm not a fan of how this problem is written. specifically, the fact that the first car mentioned is called "B" and the second is called "A".

that's a pretty underhanded trick——it's probably the only reason the poster above got the wrong answer——and GMAC would do no such thing. (cf. problem #207 in OG 13th/2015, in which "Car A" and "Car B" are named in the order in whch normal people would name them.)

i'll see whether i can get this changed. GMAC's problems are often hard, but they're always written in what is basically the most straightforward way possible. so, our problems should reflect that standard, too.