Question

The 10,000-meter long-distance running event in the summer Olympics is approximately 6.2 miles. Which equation could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute?

Answer 1

Answer:

$\bold{t = f(s) = \dfrac{6.2}{s}}$

Step-by-step explanation:

Given that distance is 10,000 meter or 6.2 miles.

Time taken is $t$ minutes.

Average speed is $s$ miles/minutes

To find:

Equation to determine time 't' as a function of average speed 's' = ?

t is in minutes and

s is in miles/minute

Solution:

First of all, let us have a look at the formula for Average Speed:

$\text{Average Speed} = \dfrac{\text{Total Distance Traveled}}{\text{Total Time Taken}}\\\Rightarrow \text{Total Time Taken} = \dfrac{\text{Total Distance Traveled}}{\text{Average Speed}}$

Now, we are given that Time, $t$ should be in minutes and

Average speed, $s$ must be in miles per minute

That means, we must have distance in miles.

Putting all the values in above formula.

So, the formula or equation becomes:

$t = \dfrac{6.2}{s}$

Therefore the equation to find time, $t$ in minutes as a function of Average Speed, $s$ is given as:

$\bold{t = f(s) = \dfrac{6.2}{s}}$