according to modern science, earth is about 4.5 billion years old and written human history extends back…

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. complete parts a and b.\na. how much time on the clock represents 500 million years?\n1.333 hour(s)\n(round to three decimal places as needed.)\nb. how long before noon does written human history begin?\n□ second(s)\n(round to three decimal places as needed.)

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. complete parts a and b.\na. how much time on the clock represents 500 million years?\n1.333 hour(s)\n(round to three decimal places as needed.)\nb. how long before noon does written human history begin?\n□ second(s)\n(round to three decimal places as needed.)

Answer

Explanation:

Step1: Find the ratio for part a

Set up a proportion. Let $x$ be the time on the clock for 500 million years. The ratio of 500 million years to 4.5 billion years should be the same as the ratio of $x$ hours to 12 hours. First, convert 4.5 billion to 4500 million. The proportion is $\frac{500}{4500}=\frac{x}{12}$.

Step2: Solve the proportion for part a

Cross - multiply: $4500x = 500\times12$. Then $4500x=6000$, and $x=\frac{6000}{4500}=\frac{4}{3}\approx1.333$ hours.

Step3: Find the ratio for part b

Let $y$ be the time on the clock for 10000 years. Convert 4.5 billion years to 4500000000 years and 10000 years to 10000 years. The proportion is $\frac{10000}{4500000000}=\frac{y}{12}$.

Step4: Solve the proportion for part b

Cross - multiply: $4500000000y = 10000\times12$. So $4500000000y = 120000$, and $y=\frac{120000}{4500000000}=\frac{1}{37500}$ hours. Since 1 hour = 3600 seconds, then $y=\frac{1}{37500}\times3600 = 0.096$ seconds.

Answer:

a. 1.333 b. 0.096