Answer: Choice B
[tex]\frac{75 \text{ km}}{1 \text{ hr}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}}[/tex]
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Explanation:
We'll use the following facts (either memorized or written on a reference sheet somewhere)
- 1000 m = 1 km
- 1 hr = 60 min
- 1 min = 60 sec
Each of those equations will form conversion factors to help us go from km/hr to m/s. Each conversion factor is a fraction connecting the two sides of the equation. Example: The equation 1000 m = 1 km forms the conversion factor of [tex]\frac{1000 \text{ m}}{1 \text{ km}}[/tex]
In choice B, notice how the fractions are set up. The "km" units cancel when dividing. The same goes for the "hr" and "min" units.
Check out the screenshot below where I show this cancellation in action. The color-coding helps show how the terms pair up and cancel.
Choice A comes close to what choice B is saying, but we don't have the "min" units cancel. So choice A is eliminated as an answer.
Choices C and D are also eliminated because of the "75 km" in the denominator. It should be 1 km.
