Answer:
344.60 m/s
Explanation:
We can obtain the answer by simply multiplying for the correct conversion factor.
Starting with the equivalence:
[tex]1 km = 0.621 miles[/tex]
We can divide both sides by 0.621 miles:
[tex]\frac{1 km}{0.621 miles} = \frac{0.621 miles}{0.621 miles}[/tex].
Of course, the right side of this must be equal to 1.
[tex]\frac{1 km}{0.621 miles} = 1[/tex].
The left side its our conversion factor. Now, lets take our speed of sound, lets call it c:
[tex]c = 0.214 \frac{miles}{second}[/tex].
Now, let just multiplied it for our conversion factor. We can do this cause multiplying for a conversion factor its the same that multiplying by 1:
[tex]c = 0.214 \frac{miles}{second}*\frac{1 km}{0.621 miles} = 0.34460 \frac{km}{s}[/tex]
Note that we got ride of the miles! This is cause the miles appear dividing in our conversion factor, and they cancel with the miles that we got in the speed of sound.
Now, the problem its almost solved. We got the speed in kilometers, and we need to convert this to meters, luckily, we know that 1 kilometer its 1000 meters, and we can, again, got a conversion factor:
[tex]1 km = 1000 m[/tex]
Of course, now we want to make those kilometers disappear and left only the meters, so, we divide by 1 km on each side:
[tex]1 = \frac{1000 m}{1 km}[/tex]
multiplying our speed of sound by this conversion factor, we get
[tex]c = 0.34460 \frac{km}{s}*\frac{1000 m}{1 km} = 344.60 \frac{m}{s}[/tex]
