The tortoise and the hare are having a race. In this tale, the tortoise moves at 50 feet per hour while the hare moves at 250 feet per hour. The tortoise takes 8 hours longer than the hare to finish. What was the distance of the race?

a. Let (t) represent the unknown time in hours that it took the hare to complete the race. Write an expression (not an equation!) representing the time it took the tortoise to finish the race.

b. Write two equations that represent the race, one for the hare and one for the tortoise.

c. What is the distance of the race?

a. Let's use the variable (t) to represent the time in hours that it took the hare to complete the race. Since the tortoise takes 8 hours longer to finish, the time it took the tortoise can be expressed as (t+8).

b. The equation representing the hare's race can be written as: Distance = Speed x Time. Therefore, the equation for the hare is: Distance = 250t.

For the tortoise, the equation can be written as: Distance = Speed x Time. Therefore, the equation for the tortoise is: Distance = 50(t+8).

c. In order to find the distance of the race, we need to set the two equations equal to each other because both the hare and tortoise reach the same distance at the end of the race:
250t = 50(t+8).

Now, we can solve this equation to find the value of (t), which represents the time it took for the hare to complete the race.

a. To represent the time it took the tortoise to finish the race, we can use the equation t + 8, where t represents the time in hours it took the hare to complete the race. Since the tortoise takes 8 hours longer than the hare, we add 8 to the hare's time to get the tortoise's time.

b. Let's write two equations to represent the race:
For the hare:
Distance = Speed × Time
Distance = 250t

For the tortoise:
Distance = Speed × Time
Distance = 50(t + 8)

c. Now we need to find the distance of the race. Since both the hare and the tortoise covered the same distance, we can set their distance equations equal to each other:
250t = 50(t + 8)

To solve this equation for t, we will first distribute the 50 on the right side:
250t = 50t + 400

Next, we will subtract 50t from both sides of the equation to isolate the t variable:
200t = 400

Finally, we can divide both sides by 200 to solve for t:
t = 400/200
t = 2

So, it took the hare 2 hours to complete the race. We can substitute this value into the hare's distance equation to find the distance of the race:
Distance = 250t
Distance = 250(2)
Distance = 500 feet

Therefore, the distance of the race is 500 feet.

hare is 5 times faster, so the tortoise takes 5 times as long: 5t

since time = distance/speed,
1/5t = 1/t + 8
find t, and then the distance is t*250