A tortoise can run with a speed of 16.0 cm/s, and a hare can run exactly 25 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 cm.

(a) How long does the race take?
(b) What is the length of the race?

OMG !! i was suck on this question for like a billion years !! and i still havent gotten the answer!:(

Look at the time when you posted this question. Can you figure out why there's no physics tutor online then?

speed of tortoise = 16 cm/s

speed of hare = 25(16) or 400 cm/s

let the time for tortoise be t seconds
then time for hare = t-120 seconds

distance for tortoise = 16t
distance for hare = 400(t-120)
but they went the same distance, so ....
400(t-120) = 16t
400t - 48000 = 16t
384t = 48000
t = 125

the race took 125 seconds or
2 minutes and 5 seconds

the length of the race was 16t = 16(125) = 2000 cm or 20 metres.

To solve this problem, we can use the formula: distance = speed x time.

Let's start by finding the speed of the hare. Given that the tortoise's speed is 16.0 cm/s, the hare's speed is 25 times faster, which gives us a speed of 25 x 16.0 cm/s = 400.0 cm/s.

(a) To find how long the race takes, we need to calculate the time it takes for both the tortoise and the hare to complete the race.

Let's assume the time taken by the tortoise is t seconds. The distance covered by the hare in t seconds would be 400.0 cm/s x t = 400t cm.

However, the hare stops to rest for 2.00 min, which is equivalent to 120 seconds. Therefore, the time taken by the hare is t + 120 seconds.

The distance covered by the tortoise would be 16.0 cm/s x t = 16t cm.

We are given that the tortoise wins the race by 20.0 cm, so we can set up the following equation:
distance covered by tortoise = distance covered by hare + 20.0 cm

16t cm = 400t cm + 20.0 cm

Rearranging the equation to solve for t:
384t cm = 20.0 cm

t = 20.0 cm / 384 cm

t ≈ 0.0521 s

Now, we can find the total time taken for the race:
Total time taken = t + 120 sec

Total time taken ≈ 0.0521 s + 120 s

Total time taken ≈ 120.0521 s

Therefore, the race takes approximately 120.0521 seconds.

(b) To find the length of the race, we can use the distance formula mentioned earlier.

The distance covered by the tortoise would be 16.0 cm/s x t = 16t cm.

We already calculated the value of t to be approximately 0.0521 s, so the distance covered by the tortoise would be 16.0 cm/s x 0.0521 s ≈ 0.8336 cm.

Therefore, the length of the race is approximately 0.8336 cm.