Question

. A tortoise and a hare are having a race. The tortoise moves at 4 miles per hour. The hare travels at 10 miles per

hour. Halfway through the race, the hare decides to take a 5-hour nap and then gets up and continues at 10 miles
per hour.
a. If the race is 40 miles long, who won the race? Support your answer with mathematical evidence.
b. How long (in miles) would the race have to be for there to be a tie between the two creatures, if the same
situation (as described in Exercise 1) happened?

Answer 1

a. hare won the race.

b. race would be 33.33 miles long to be tie.

Explanation:

The speed of tortoise = 4 miles per hour.

and the speed of hare = 10 miles per hour

a. If the race is 40 miles long.

Tortoise complete the race =
`(40)/(4)`

= 10 hours

Hare complete the race =
`(40)/(10)`

= 4 hours

Hare took a 5-hour nap so his race completed = 4 + 5 = 9 hours

Therefore, Hare won the race.

b. Let the distance of race = x miles

Time taken by tortoise will be =
`(distance)/(speed)`

=
`(x)/(4)` hours

Time taken by hare to cover x miles and 5 hours nap =
`((x)/(10)+5)`

If time take by both the two creatures are same.

`(x)/(10)+5` =
`(x)/(4)`

`(x)/(4)` -
`(x)/(10)` = 5

`(5x-2x)/(20)` = 5

`(3x)/(20)` = 5

3x = 100

x =
`(100)/(3)`

x = 33.33 miles

The race would be 33.33 miles to be a tie.