Question

For my assignment I am given this:
1760 yds = 1 mi
1 km = 0.6214 mi
12 in = 1 ft
3 ft = 1 yd
2.54 cm = 1 in
60 s = 1 min
60 min = 1 h
Convert 5.25 cm/s to mi/h
I have spent like two hours trying to do this. I can't figure it out and my teacher isn't getting back to me. I need help! I will give a medal!

Answer 1

Okay! Let's do a little tut on the factor-label method of conversion, using those magnificent conversion factors they gave you!

First thing we want to do is figure out that there are two conversions we'll want to make. We need to get centimeters to miles and seconds to hours. That's going to take a bit of converting, but we'll be fine. Let's get our original factor up:
\[\frac{ 5.25 cm }{ 1 s }\]
Pretty, right? Let's start by converting the length measurement. From the conversion factors you have, we see that we can convert kilometers to miles. There's no conversion factor for centimeters, but that'll be all right, we know the metric system!

1 cm is equal to 0.01 m, which is equal to 0.00001 km. You can check that with the factor-label method too, but that makes it unnecessarily long, IMO. Now we have our conversion factor that we multiply our number by:
\[\frac{ 5.25 cm }{ 1 s } \times \frac{ 0.00001km }{ 1 cm }\]
That's nice, the centimeters cancel to give us km/s. Now we get it to miles:
\[\frac{ 5.25 cm }{ 1 s } \times \frac{ 0.00001km }{ 1 cm } \times \frac{ 0.6214 mi }{ 1 km }\]
Now we have both centimeters and kilometers cancelling to give us mi/s. But we need mi/h, so we need another conversion factor. There are 86400 s in an hour (Google it if you don't believe any of this stuff I pull out of thin air), so that's our last conversion factor:
\[\frac{ 5.25 cm }{ 1 s } \times \frac{ 0.00001km }{ 1 cm } \times \frac{ 0.6214 mi }{ 1 km } \times \frac{ 86400 s }{ 1 h}\]
Yay, the centimeters, kilometers, and seconds cancel out to give us mi/h. Now we just need to multiply everything together to get the final result (which I'll leave to you to compute. Does all of this make sense? Do you have any questions?

Answer 2

Thank you so much!! That made so much more sense to me then what I was thinking. To get the answer I multiply everything on the top and then divide by 1 since all the denominators are 1 correct?

Answer 3

Wait no, I just tried that and the answer made no sense

Answer 4

How would I get the answer?

Answer 5

That should be how you get it. I messed up, it's 3600 seconds in an hour, and 86400 second in a day. That was the problem. using 3600 I get the 0.177 that Google gets.