Question

A satellite can move at 17,000 miles per hour. How many hours will it take to reach a star that is three light years away? Recall that 1 light year = 9.5 ∙ 1012 kilometers and 1 kilometer = 0.62 miles. Show your work.

Answer 1

First convert the distance to miles 

9.5 × 10^12 km x 0.62 miles/km 
= (0.62 × 9.5) x 10^12 miles 
= 5.9 × 10^12 miles 

But we want to triple that, because it is 3 light years (not just 1): 
3 x 5.9 × 10^12 miles 
≈ 18 × 10^12 miles 
≈ 1.8 × 10^13 miles 

Next divide by the speed to get the time (in hours). 
t = 1.8 × 10^13 miles / 17000 miles/hour 

Let's convert the speed to scientific notation: 
t = 1.8 × 10^13 / 1.7 x 10^4 

t = (1.8 / 1.7) × (10^13 / 10^4) <-- when dividing powers with the same base, subtract the exponents 
t ≈ 1.1 × 10^9 

Let's convert that back to standard notation. 

Answer: 
1,100,000,000 hours

Answer 2

Answer:

1 light year = 9.5 * 10^12 kilometers

1 light year = 5.9 * 10^12 miles

3 light years:

3 * 5.89 * 10^12 miles =

1.767 * 10^12 miles =

1.767 * 10^13 miles

How long does it take to get there?

(1.767 * 10^13) / (17000) =

(1.767 * 10^13) / (1.7 * 10^4) =

1.03941176471 * 10^9 =

1039411764.71 ≈ 1,040,000,000

It will take about 1,040,000,000 hours to get to a star that is 3 light years away.