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

`\bold{t = f(s) = (6.2)/(s)}`

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} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}\\\Rightarrow \text{Total Time Taken} = \frac{\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 = (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) = (6.2)/(s)}`