Three Digital Clocks at Different Speeds

[d-rock]

Homework Statement

Three digital clocks A, B, and C run at different rates and do not have simultaneous readings of zero. Figure 1-6 shows simultaneous readings on pairs of the clocks for four occasions:

___________312_________________512__ Clock A
___25______125_______200_______290__ Clock B
___92________________142____________ Clock C

For example, at the earliest occasion, B reads 25 s and C reads 92 s. If two events are 600 s apart on Clock A, how far apart are they on (A) clock B and (B) clock C? (C) When clock A reads 400 s, what does clock B read? (D) When clock C reads 15 s, what does clock B read? (Assume negative readings for prezero times.)

Homework Equations

Unsure other than possibly a bunch of ratios?

The Attempt at a Solution

Okay, on the little line chart I made above, any spot where the numbers are right on top/below each other is a point where sumultaneous readings are. At the first event, Clock B is at 25 seconds while Clock C is at 92 seconds, and so on.

Since the chart was somewhat easy to read, I added up the time between 312 and 512 on Clock A, and the time between 125 and 290 on Clock B:

(A) Therefore, for on Clock A there is a space of 200 seconds while Clock B has 165 seconds. For Clock A to go 600 seconds, I multiplied the space by 3, and thus did the same to Clock B's space since they are the simultaneous, thus getting a time of 495 seconds on Clock B. The answer in the book says this is correct.

The problem I have is that I have no absolute clue on what to do or what equations to use, as I obviously cannot use the above method for part B of the question.

I'm in a college-level Physics course in my 12th grade year of High School. I've no real Physics knowledge although I have taken one part of Calculus. We have not been tought much yet but the teacher allows us to call him if we need help. I cannot reach him however and so I'm pretty much stuck.

Is there any direction that someone can at least point me in, because this is already quite confusing? I'm assuming I need some ratios or something but I cannot put it together.

This is due tomorrow and I've only had today to do it. I have other problems to do too but this is the only tough one so far.

 

[member 141513]

d d-rock,
is the line the clock interval ?

 

[Goddar]

Hey, you got it right in the first part, this is really all about ratios:
What you did there is basically: (interval B/interval A) * 600 = 495
logically, all you have to do in (b) is: (interval C/interval B) * 495 =...
This is more about logic than actual physics (except when it comes to relativity principles); good luck!

 

[d-rock]

Yeah I went into school early and was figuring out the ratio. I finally understood it so yeah, it's good now.