Question

If you complete a 10K marathon, how many miles have you traveled? Show all your math steps include units with your answer, and explain why your answer makes sense.

Answer 1

Answer:

The distance traveled is 6.21 miles

Explanation:

We know that a 10 K marathon has a length of 10 kilometers, but how many miles this is? We can find this finding the conversion factor between miles and kilometers.

Finding the conversion factor

To find the conversion factor, we start writing the equivalence between kilometers and miles:

$1 \ mi = 1.609 \ km$

Now, we can divide both side by 1.609 kilometers

$\frac{1 \ mi}{1.609 \ km } = \frac{1.609 \ km}{ 1.609 \ km}$

Now, the right side of this equation is equal to 1.

$\frac{1 \ mi}{1.609 \ km } = 1$

This is our conversion factor. Lets see how we use it:

Using the conversion factor

We know that the length L of the marathon is

$L = 10 \ km$

Now, we can multiply the length  by our conversion factor, we are allowed to do this because the conversion factor equals one, so, the physical meaning of the length is the same.

$L = 10 \ km * \frac{1 \ mi}{1.609 \ km } = 6.21 \ mi$

So, the distance traveled is 6.21 miles.