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.

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