Question

A tortoise and a hare are competing in a 1600-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second. Define a function f to represent the tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.

Answer 1

f(t) = 1090 - 5t

Explanation:

A tortoise and a hare are competing in a 1600 meter race but the tortoise is 510 meter ahead of hare.

If tortoise traveled in 't' seconds after the start gun was fired, total distance covered = Speed × times

= 5t meters

Since distance of the tortoise from the start line is = 510 meter

So, the distance at which the tortoise will reach after the start gun = (510 + 5t) meter

Now the distance of tortoise from the finish line = 1600 - (510 + 5t)

= 1600 - 510 - 5t

= (1090 - 5t)

If a function 'f' defines the tortoise's distance from the finish line then the function will be f(t) = (1090 - 5t)

Answer 2

The required function is
`f(t)=1090-5t`

Explanation:

Consider the provided information.

A tortoise and a hare are competing in a 1600-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start.

The tortoise begins crawling at a constant speed of 5 meters per second.

The distance covered by tortoise in t second is:

`Distance=speed * time`

`Distance=5* t=5t`

We need to Define a function f to represent the tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.

`f(t)=1600-510-5t`

`f(t)=1090-5t`

Hence, the required function is
`f(t)=1090-5t`