Running Around a Circle

[dtweah]

Bill and Tom start at the same place and run around an oval track in opposite directions. If they start at the same time and always run at a constant rate then they meet in one minute. If Tom starts 30 seconds before Bill then they meet 50 seconds after Bill had started. How many seconds does it take Bill to run around the track one time?
a) 85
(b) 90
(c) 175/2
d) 185/2
(e) 195/2

[francopiccolo]

I solved it, but I don't know if as fast as possible.

Let it be:

B = Tracks Bill makes per second.
T = Tracks Tom makes per second.

Then:

60B + 60T = 1
50B + 80T = 1

Working on that system, B = 1/90. That means Bill makes one track in 90 seconds.

If sbdy knows a quicker approach, pleas tell!

[dumb.doofus]

Let B be Bill's speed and T be Tom's speed..

Given:
1. When they start together they meet in 1 min.
2. When Tom has a 30 sec headstart then they meet in 50 secs..

Using the above given facts.. I can write..

(B + T)10 = 30T..

essentially meaning that whatever Tom covered in 30 secs.. B and T running together would have covered in 10 secs.. why? because when they ran together first time they covered the whole track in 60 secs.. Next time, they covered portion of the track in 50 secs.. so 10 secs they would cover what Tom alone covered in 30 secs..

The above equation gives me B = 2T.. meaning B's speed is twice that of Tom..

So that means that B would have covered twice the distance than what Tom covered when first time they ran.. so remaining distance is just 1/3rd of the total distance.. so B would take 60 + 30 secs to complete it alone..

i.e. 90 secs..

[Svedankae]

i got B as well, took me longer than two minutes though. Any indication on what difficulty level this question is?

[summersette]

can somebody explain this please using the RTD chart method. I am quite confused. thanks.