A speedy tortoise can run at .01 meters per second, and the hare can run 21 times as fast. I. A race they start at the same time, but the hare stops for 1.5 minutes so the tortoise wins by a shell(20cm).
How long is the race?
How long is the path?
Let T be the duration of the race (seconds) and X be the distance traveled to the finish line (cm).
1* T = X (distance traveled by tortoise)
21(T - 90) = X - 20 (distance traveled by hare)
First eliminate X by substitution.
21 T - 1890 = T - 20
20 T = 1870
T = 93.5 seconds
X = T = 93.5 cm
To find the length of the race, we need to determine the time it takes for the hare to catch up with the tortoise. We know that the hare is 21 times faster than the tortoise, so its speed can be calculated as follows:
Hare's speed = Tortoise's speed * 21
= 0.01 m/s * 21
= 0.21 m/s
Now, let's assume the time it takes for the hare to catch up with the tortoise is "t" seconds. During this time, the hare stops for 1.5 minutes, which is equal to 1.5 * 60 = 90 seconds. Consequently, the hare's actual running time is reduced by 90 seconds.
The distance covered by both the hare and the tortoise should be the same when the hare catches up. Using the formula "distance = speed × time", we can create two equations:
Distance covered by the hare: 0.21 m/s * (t - 90) seconds
Distance covered by the tortoise: 0.01 m/s * t seconds
Since they both cover the same distance when the hare catches up, we can equate the two equations:
0.21 m/s * (t - 90) = 0.01 m/s * t
Simplifying the equation, we get:
0.21t - 18.9 = 0.01t
Subtracting 0.01t from both sides:
0.2t - 18.9 = 0
Adding 18.9 to both sides:
0.2t = 18.9
Finally, dividing both sides by 0.2:
t = 94.5 seconds
Therefore, the time it takes for the hare to catch up with the tortoise is 94.5 seconds. Since the hare stops for 90 seconds during the race, the total race time is 94.5 + 90 = 184.5 seconds.
To calculate the length of the path, we can use the tortoise's speed and the total race time:
Path length = Tortoise's speed * Total race time
= 0.01 m/s * 184.5 seconds
= 1.845 meters
Hence, the length of the race is 184.5 seconds, and the length of the path is 1.845 meters.