We are given that the velocity of a hare is 6 km/h faster than the velocity of a tortoise. We can represent this as follows:
Now, we are also given that the hare travels 40 km using the same time it takes the tortoise to travel 10 km. Since the distance is the product of the velocity by the time, we have:
Where:
Now, we divide both equations:
Since the time is the same we can cancel out "t":
Simplifying the fraction:
Now, we multiply both sides by the velocity of the tortoise:
Now, we substitute this value in the first equations, we get:
Now, we subtract the speed of the tortoise from both sides:
Solving the operations:
Now, we divide both sides by 3:
Therefore, the velocity of the tortoise is 2 km/h.
Now, since the velocity of the hare is 4 times the velocity of the tortoise, we have:
Therefore, the velocity of the hare is 8 km/h.