Time = distance/speed conversion problem

[Mathnomalous]

Homework Statement

The velocity of light is 1.86 x 10⁸ mi/hr. The distance of Mercury from the Sun is approximately 5.78 x 10⁷ km. How many minutes will it take for light from the Sun to travel to Mercury?

Homework Equations

1 mi = 1.609 km
time = distance/speed
60 min/1 hr

The Attempt at a Solution

1.609 km/1 mi * 1.86 x 10⁸ mi/hr = 2.99 x 10⁸ km/hr

time = 5.78 x 10⁷ km / 2.99 x 10⁸ km/hr = 1.933 x 10^-1 hr

60 min/1 hr * 1.933 x 10^-1 hr = 115.98 x 10^-1 min

Answer: 11.598 minutes.

That answer does not make sense to me. What did I do wrong here?

 

[rock.freak667]

I think you converted km to mi incorrectly.

1 kilometer = 0.621371192 miles

 

[HallsofIvy]

I think you converted km to mi incorrectly.

1 kilometer = 0.621371192 miles

Yes, so one mile is 1/.621371192 km= 1.60934400 miles which is what he used. And he was converting from miles to kilometers.

However, Mathnomolous, the speed of light is 1.86 x 10⁸ miles per second, not miles per hour!

You should have divided by 60 to convert second to minutes, not multiplied to convert hours to minutes.

 

[Vasara]

Your speed of light is incorrect. It's not 2.99 x 10⁸ km/hr, it's 2.99 x 10⁸ m/s, which is something like 6.71 x 10⁸ mi/hr or 186,000 miles per second.

 

[Mathnomalous]

I typed the problem as it appears on my chemistry textbook. I also asked the professor to do the problem in class, with the same result. I never imagined the textbook had that kind of error. Thanks for the correction. I should be able to obtain the right answer now.