The data below represents simulataneous readings on pairs of clocks (8c1p15) Thr

Question

The data below represents simulataneous readings on pairs of clocks

(8c1p15) Three digital clocks A, B, C run at different rates and do not have simultaneous readings of zero. The table shows simultaneous readings on pairs of clocks for four occasions. (At the earliest occasion, for example, B reads 25 s and C reads 93 s) If two events are 600 sapart on clock A, how far apart are they on clock B?

how far apart are they on clock C?

When clock A reads 400 s, what does clock B read?

When clock C reads 15 s, what does clock B read? (Assume negative readings for prezero times.)

Explanation / Answer

If two events are 600 s apart on clock A, how far apart are they on clock B?
(time on clock b)/(time on clock a)

= (290-125)/(674.08 - 393.25)=165/280.83

=0.587544

now multiply this by 600 and get
352.5264 s on clock B


(time on clock c)/(time on clock a)=
((time on clock c)/(time on clock b))*((time on clock b)/time on clock a))


(time on clock c)/(time on clock b)=
(141-92.785)/(200-25)= 48.215/175=0.2755

so (time on clock c)/(time on clock a)=
(48.785/175)(165/280.83)=0.1618
multiply this by 600 and get 97.121 s on clock C


for 400 secounds
(165/280.83)400= 235.017 s on clock A

15/(48.785/175) = 53.8 s on clock B

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