Question

A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

• A. 9 : 5
• B. 5 : 9
• C. 4 : 7
• D. 3 : 5

Answer 1

Answer:

A. 9 : 5

Understanding the Problem: Ratio of Speeds

• This problem involves comparing the speeds of two animals, a dog and a hare, based on their leaps and the distance covered by each leap.

• The core concept is that Speed = Distance / Time. When comparing speeds, if the time taken is the same, the ratio of speeds is equal to the ratio of distances covered.

Step-by-Step Explanation:

• Given Information:

  • Dog takes 3 leaps for every 5 leaps of the hare. This implies that in the same amount of time, the dog makes 3 leaps while the hare makes 5 leaps.

  • One leap of the dog is equal to 3 leaps of the hare in terms of distance.

• Let's denote:

  • Length of 1 dog's leap as L_D

  • Length of 1 hare's leap as L_H

• Establishing Leap Length Equivalence:

  • From the second given fact, we know: L_D = 3 * L_H.

• Calculating Total Distance Covered in Same Time:

  • Assume a unit of time (e.g., 1 minute) during which the dog takes 3 leaps and the hare takes 5 leaps.

  • Distance covered by the dog:
    Number of leaps by dog × Length of 1 dog's leap
    = 3 × L_D
    = 3 × (3 * L_H) (Substituting L_D = 3L_H)
    = 9 * L_H

  • Distance covered by the hare:
    Number of leaps by hare × Length of 1 hare's leap
    = 5 × L_H
    = 5 * L_H

• Determining the Ratio of Speeds:

  • Since both distances are covered in the same amount of time, the ratio of their speeds will be the ratio of the distances they cover.

  • Ratio of (Speed of Dog) : (Speed of Hare)
    = (Distance covered by Dog) : (Distance covered by Hare)
    = (9 * L_H) : (5 * L_H)

  • Cancelling out L_H from both sides, we get the ratio: 9 : 5.