Question

56. Universal Clock.
According to modern science, Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose you represent the entire history of Earth by 12 hours on a clock, with the birth of Earth at the stroke of midnight and today at the stroke of noon.
a. How much time on the clock represents 1 billion years?
b. At what time on the clock does written human history begin?
The answer to part (b) should be determined up to a hundred of a "second."

Answer 1

*

Answer 2

start with
12 hours = 4.5 billon years

Answer 3

My answer to part A is 1 billion years x (12 hours/4.5 billion years)
=2 and 2/3 hours, or 2 hours and 40 minutes.

But I'm still lost on part B

Answer 4

well you've got a)right

how many times does 10 000 go into 45 000 000 000?

Answer 5

ok so 4.5 billion yr / 10,000 yr = 450,000 or 4.5 x 10^5

Answer 6

so what is 2hr 40 mins divided by this

Answer 7

But doesnt 2 hr 40 min represent 1 billion years? And written human history is only 10,000 years?

Answer 8

oh, right

Answer 9

ok i made a few mistakes here, lets start part b) again

Answer 10

Ok. Thank you for the help

Answer 11

how many times does 10 000 go into 1 000 000 000

Answer 12

10^4 -----> 10^9

Answer 13

100,000 or 1 x 10^5

Answer 14

so 2hr 40mins divided by 10^5 = time since humans poped into existence

Answer 15

0.0016?

Answer 16

what are your units?

Answer 17

I don't know now haha. I'm confused why we are using 1 billion years/2 hours 40 min. instead of just the 10,000 years

Answer 18

This was my original answer that I'm pretty sure is wrong...
(10,000 years/ 4.5 billion years) = (1 x 104 yr / 4.5 x 109 yr)
= 2.22 x 10-6
or 0.00000222

Answer 19

* (10,000 years/ 4.5 billion years) = (1 x 10^4 yr / 4.5 x 10^9 yr)
= 2.22 x 10^-6
or 0.00000222

Answer 20

but that wouldn't leave me with hundred of a second as my final units.. so I'm not sure where to bring in the time part..

Answer 21

This was an example in my textbook

Answer 22

\[12[\text{hr}]=4.5\times10^9[\text {yr}]\]
\[\frac{12}{4.5}[\text{hr}]=2\tfrac23[\text{hr}]=10^9[\text {yr}]\]

Answer 23

\[2\tfrac23[\text{hr}]\times10^{-5}=10^4[\text {yr}]\]
\[2\tfrac23[\text{hr}]\times10^{-5}\times\frac{3600[\text s]}{[\text{hr}]}=10^4[\text {yr}]\]

Answer 24

Ok i understand the first part but not sure about the second, does this work?
10,000 years x (12 hours/4.5 billion years) x (60 min/1 hour) x (60 sec / 1 min) = .096 seconds

Answer 25

that s what im getting , ~ 0.1 second

Answer 26

ah great! So in terms of time on the clock it would be 12 hours - 0.96 seconds?

Answer 27

i can remember a slightly different result

Answer 28

or wait, it would be 11:60 - .0096 because its .096 of a min. not a second, so 11:59:904 would be the final time I think?

Answer 29

oh

Answer 30

that looks right, but im not having a great day so if theres a mistake i cant see it.

Answer 31

Ok, well this is much further than I was before regardless so thank you so much for all of the help! This is my first time using this site - how can I award you points or something? Just click best response?

Answer 32

yeah, if you want to

( there is an option to become a fan as well , if you click on someones name)

I like how you've showed working so ill be your fan

(im usually more on my game than today) see you next time

Answer 33

[i think i remember doing a very similar question before and getting 13 seconds as the answer, but i think that was how long humans have existed, not how long human written history has exited] so i think you've worked this out right \(\checkmark\)

Answer 34

Just wanted to mention that I received full credit for this problem/all calculations were correct. Thanks again for the help!

Answer 35

Great stuff!\[\boxed{\huge\color{red}\checkmark}\]