Math Help - Conversions (cm/sec to km/day)

An object travels at a speed of 7500 cm/sec. How far will it travel in kilometers in one day?

First, it is required that I have a unit plan
(Ex. mm -> cm -> meters)

Second, I must show the conversion factors
(Ex. 10mm/1cm, 100cm/1meter)

Third, I must perform and solve the problem using my conversion factors.
(Ex. They want me to convert 1meter to mm. Using my conversion factors, it looks like this: 1m x 100cm/1m x 10mm/1cm. The answer is 1000mm = 1meter)

*note: obviously, the example I used has nothing to do with the problem I am currently struggling with (the one in bold).

To solve the bold problem, I first need to come up with a unit plan... but I don't know how to with this one. Please help me

(This is actually chemistry work I am doing)

We know that there are 24 hrs in a day, 60 min in a hr, and 60 sec in an min. Putting all this together, we get:

1day*24hr/day*60min/hr*60sec/min

86,400 sec in a day.

No we can solve your question.

d = v*t

d = 7500cm/sec * 86,400sec

d = 648,000,000 cm/sec


To convert cm to km, we know that:

1cm = 1/100m and
1m = 1/1000km

So, we multiply these two fractions to get

1cm = 1/100000km


Finally, we multiply this conversion factor by our answer to get our answer in km.

648,000,000/100,000 = 6480km in one day.

When we multiply v (which is in cm/sec) by t (which is in sec) we are left with the unit of cm.

Hopefully this makes sense.