Answer:
The spaceship will get to Alpha Centaur in time
Step-by-step explanation:
<u><em>The complete question in English is</em></u>
You're the commander of a spaceship. Your mission is to reach Alpha Centaur in five years. The distance from the sun to Alpha Centaur is 2.5 x 10^13 miles. The distance from Earth to Sun is approximately 9.3 x 10^7
miles. Your spaceship can travel at the speed of light. You know that light can travel a distance of 5.88 x 10^12 miles in a year. Can you get to Alpha Centaur in time?
step 1
Find the time it takes for the spaceship to travel from Earth to the Sun
The distance from the Earth to Sun is equal to
![9.3*10^7\ miles](https://tex.z-dn.net/?f=9.3%2A10%5E7%5C%20miles)
The spaceship can travel at the speed of light
The light can travel a distance of
in a year
so
using a proportion
![\frac{5.88*10^{12}\ miles}{1\ year}=\frac{9.3*10^7\ miles}{x}\\\\x=(9.3*10^7)/5.88*10^{12}\\\\x=1.58*10^{-5} \ years](https://tex.z-dn.net/?f=%5Cfrac%7B5.88%2A10%5E%7B12%7D%5C%20miles%7D%7B1%5C%20year%7D%3D%5Cfrac%7B9.3%2A10%5E7%5C%20miles%7D%7Bx%7D%5C%5C%5C%5Cx%3D%289.3%2A10%5E7%29%2F5.88%2A10%5E%7B12%7D%5C%5C%5C%5Cx%3D1.58%2A10%5E%7B-5%7D%20%5C%20years)
This time is very small in years
Convert to minutes
![1.58*10^{-5} \ years=1.58*10^{-5} (365)(24)(60)=8.3\ min](https://tex.z-dn.net/?f=1.58%2A10%5E%7B-5%7D%20%5C%20years%3D1.58%2A10%5E%7B-5%7D%20%28365%29%2824%29%2860%29%3D8.3%5C%20min)
step 2
Find the time it takes for the spaceship to travel from the Sun to Alpha Centaur
The distance from the the Sun to Alpha Centaur is equal to
![2.5*10^{13}\ miles](https://tex.z-dn.net/?f=2.5%2A10%5E%7B13%7D%5C%20miles)
The spaceship can travel at the speed of light
The light can travel a distance of
in a year
so
using a proportion
![\frac{5.88*10^{12}\ miles}{1\ year}=\frac{2.5*10^{13}\ miles}{x}\\\\x=(2.5*10^{13})/5.88*10^{12}\\\\x=4.25\ years](https://tex.z-dn.net/?f=%5Cfrac%7B5.88%2A10%5E%7B12%7D%5C%20miles%7D%7B1%5C%20year%7D%3D%5Cfrac%7B2.5%2A10%5E%7B13%7D%5C%20miles%7D%7Bx%7D%5C%5C%5C%5Cx%3D%282.5%2A10%5E%7B13%7D%29%2F5.88%2A10%5E%7B12%7D%5C%5C%5C%5Cx%3D4.25%5C%20years)
![4.25\ years< 5\ years](https://tex.z-dn.net/?f=4.25%5C%20years%3C%205%5C%20years)
therefore
The spaceship will get to Alpha Centaur in time