A tortoise and a hare race against each other. A hare runs at a constant speed of 36 km per hour for exactly ten seconds and waits for the tortoise to catch up. If the tortoise takes two hours to move 1 km, how long will it take to catch up?
well, how far does the hare go?
distance = speed * time
what do I multiply
36 * 10 ?
not quite. You have to watch the units. 10 seconds is 1/360 hours.
To find out how long it will take the hare to catch up to the tortoise, we need to determine how far the tortoise can travel in the time it takes for the hare to run for ten seconds.
First, let's convert the hare's constant speed from kilometers per hour to meters per second. Since there are 1000 meters in a kilometer and 3600 seconds in an hour, the hare's speed is 36,000 meters per 3600 seconds, which simplifies to 10 meters per second.
Next, we need to calculate the distance the hare travels in ten seconds. We can multiply its speed of 10 meters per second by the time of 10 seconds:
Distance = Speed × Time
Distance = 10 meters/second × 10 seconds
Distance = 100 meters
Therefore, the hare can run 100 meters in ten seconds.
Now, let's find out how long it takes the tortoise to cover 1 kilometer. Given that it takes the tortoise two hours to cover 1 kilometer, we need to convert this time to seconds. There are 60 minutes in an hour and 60 seconds in a minute, so two hours is equal to 2 × 60 × 60 = 7200 seconds.
Now, we can determine the time it takes for the hare to catch up to the tortoise. Since the hare covers 100 meters in ten seconds, it will take the tortoise 100 meters to move from its starting position to the position the hare reached in just ten seconds.
The tortoise covers 1 kilometer (1000 meters) in 7200 seconds, so the time it takes to cover 100 meters can be found using the proportion:
Time for 100 meters = (Time for 1 kilometer ÷ 1000 meters) × 100 meters
Time for 100 meters = (7200 seconds ÷ 1000 meters) × 100 meters
Time for 100 meters = 7.2 seconds
Therefore, the hare will catch up to the tortoise in approximately 7.2 seconds.