If Jim could drive a Jetson's flying car at a constant speed of 240 km/hr across oceans and space, approximately how long would he take to drive to a nearby star that is 9.2 light-years away?

Question

If Jim could drive a Jetson's flying car at a constant speed of 240 km/hr across oceans and space, approximately how long (in millions of years, in 10⁶ years) would he take to drive to a nearby star that is 9.2 light-years away? Use 9.461 × 10¹² km/light-year and 8766 hours per year (365.25 days).

Answer 1

This is a rate problem. Rate problems have the basic formula: Rate = distance/time. This basic formula may be rearranged to solve for any unknown part using basic algebra techniques. The question asks “how long?” so we are looking for time. Solving the basic equation for time gives: time = distance/rate

This problem is a little more difficult than the basic rate problem because of the mixed units in the problem requiring that you also do some unit conversions. Remember, a light-year (ly) is a measure of distance, just as km is a measure of distance, so 9.461 × 10¹² km/light-year, is a conversion factor for converting ly to km. Because the rate (speed) is in km/hr, the distance must be in km also, so the first step is to convert ly to km: (9.2 light-years) (9.461 × 10¹² km/light-year) = 8.7 × 10¹³ km = distance

Time = distance/speed = (8.7 × 10¹³ km)/(240 km/hr) = 3.6 × 10¹¹ hr (Reminder: treat units like variables in algebra – when dividing units where one or more of the units is a “fraction”, invert the denominator and multiply). This gives us the time, but in hours. The question asks for the time in millions of years, so now need to convert hours to years, using the conversion factor 8766 hr/yr.  Because the units are currently given in hours, the question asks for (millions of) years, and the conversion factor is given as hours per year, we need to divide the number of hours by the conversion factor: 

time (in years) = (3.6 × 10¹¹ hr)/( 8766 hr/yr) = 4.1 × 10⁷ years

the units are now in years, but still not in the units asked for in the question; the final step is to divide the time in years by 10⁶ years/million years, which gives the final answer as the trip takes 41 million years.