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

Answer:

$1.03\times10^{9}$ hours will it take to reach a star that is three light years away.        

Step-by-step explanation:

Given : A satellite can move at 17,000 miles per hour.

To find : How many hours will it take to reach a star that is three light years away?

Solution :

We have given,

1 light year = $9.5\times 10^{12}$ kilometer.

1 kilometer = 0.62 miles.

1 light year = $9.5\times 10^{12}\times 0.62$ miles.

1 light year = $5.89\times 10^{12}$ miles.

The distance covered is $5.89\times 10^{12}$ miles.

The speed of satellite is 17,000 miles per hour.

Time taken is given by,

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$\text{Time}=\frac{5.89\times 10^{12}}{17000}$

$\text{Time}=\frac{589}{17}\times10^{12-5}$

$\text{Time}=34.64\times10^{7}$

The time taken in 1 light year is $34.64\times10^{7}$ hours.

For 3 light year $103.92\times10^{7}$ hours.

For 3 light year $1.03\times10^{9}$ hours.

Therefore, $1.03\times10^{9}$ hours will it take to reach a star that is three light years away.

Answer 2

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 

 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 

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 

convert that back to standard notation. 

Answer: 
1,100,000,000 hours (P.S. That is about 120,000 years).
Hope this helps!!!