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04 Mar 2024, 09:40
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A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey, and the predator covers as much distance in 2 leaps as 3 leaps of the prey. What is the ratio of the speed of the predator to that of the prey?
A. 11 : 9
B. 10 : 9
C. 1 : 1
D. 9 : 10
E. 9 : 11
A. 11 : 9
B. 10 : 9
C. 1 : 1
D. 9 : 10
E. 9 : 11
04 Mar 2024, 09:40
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Official Solution:
A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey, and the predator covers as much distance in 2 leaps as 3 leaps of the prey. What is the ratio of the speed of the predator to that of the prey?
A. 11 : 9
B. 10 : 9
C. 1 : 1
D. 9 : 10
E. 9 : 11
Assuming one leap of the predator is \(x\) units and one leap of the prey is \(y\) units, then:
In 4 leaps, the predator covers the distance of \(4x\) units.
In 6 leaps, the prey covers the distance of \(6y\) units.
Note that these distances take the predator and the prey the same amount of time.
Since it is also given that the predator covers as much distance in 2 leaps as the prey does in 3 leaps, we get \(2x = 3y\). Substituting \(2x = 3y\) in the above, we get \(6y = 2(3y) = 4x\).
Thus, in the same time period, both the predator and the prey cover the same distance of \(4x\) units, indicating an equal speed.
Answer: C
A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey, and the predator covers as much distance in 2 leaps as 3 leaps of the prey. What is the ratio of the speed of the predator to that of the prey?
A. 11 : 9
B. 10 : 9
C. 1 : 1
D. 9 : 10
E. 9 : 11
Assuming one leap of the predator is \(x\) units and one leap of the prey is \(y\) units, then:
In 4 leaps, the predator covers the distance of \(4x\) units.
In 6 leaps, the prey covers the distance of \(6y\) units.
Note that these distances take the predator and the prey the same amount of time.
Since it is also given that the predator covers as much distance in 2 leaps as the prey does in 3 leaps, we get \(2x = 3y\). Substituting \(2x = 3y\) in the above, we get \(6y = 2(3y) = 4x\).
Thus, in the same time period, both the predator and the prey cover the same distance of \(4x\) units, indicating an equal speed.
Answer: C
22 May 2024, 11:12
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Predator takes 4 leaps, while prey 6 leaps. This is equal to:
Predator takes 2 leaps, while prey 3 leaps.
Then draw these on the paper: the 2 leaps (predator) and 3 leaps (prey). Obviously, at this point the distances covered by both are not equal, just draw.
But, surprisingly, the 2 leaps (predator) and 3 leaps (prey) are equal by the second piece of information given. So the distances are equal. Therefore, if both cover the same distance in a equal period of time, their speeds are the same.
Predator takes 2 leaps, while prey 3 leaps.
Then draw these on the paper: the 2 leaps (predator) and 3 leaps (prey). Obviously, at this point the distances covered by both are not equal, just draw.
But, surprisingly, the 2 leaps (predator) and 3 leaps (prey) are equal by the second piece of information given. So the distances are equal. Therefore, if both cover the same distance in a equal period of time, their speeds are the same.
