Question

The speed of light in a vacuum is 2.998 × 108 m/s. What is its speed in miles per minute (mi/min)?

Answer 1

Task:

The speed of light in a vacuum is $2.998 \times 108 \, \text{m/s}$. What is its speed in miles per minute (mi/min)?

Solution:

To convert m/s to mi/min we have to find conversion factor first

1 mile = 1609.344 m

1m = 1/1609.344 miles

1 min = 60 s

1s = 1/60 min

Let's put mi/min instead of m/s according to equations above

$$\mathrm{m/s} = \left[ \frac{1}{1609.344} \text{ miles} \right] / \left[ \frac{1}{60} \text{ min} \right]$$

The conversion factor is

$$f = 60 / 1609.344$$

Now we can convert m/s to mi/min

$$V \text{ (mi/min)} = 2.998 \cdot 10^{8} \, \text{m/s} \cdot f = 2.998 \cdot 10^{8} \cdot (60 / 1609.344) = 1.118 \cdot 10^{7} \, \text{mi/min}$$

Answer: $V = 1.118 \cdot 10^{7} \, \text{mi/min}$