Leaps and stride length → speed ratio: A cat takes 5 leaps for every 4 leaps of a dog. Also, 3 dog leaps cover the same distance as 4 cat leaps. Find the ratio of the cat’s speed to the dog’s speed.

Introduction / Context:Speed equals strides per unit time multiplied by stride length. We are given a frequency ratio (leaps per equal time) and a stride-length relation between the animals. Combine both to obtain the speed ratio.

Given Data / Assumptions:

• Cat leaps : Dog leaps (in same time) = 5 : 4.
• 3 dog leaps = 4 cat leaps (distance equality).
• All leaps occur over the same time window used for the frequency comparison.

Concept / Approach:Let Lc and Ld be cat and dog leap lengths. From 3Ld = 4Lc ⇒ Ld = (4/3)Lc. Speeds over the same time T: Vc : Vd = (5Lc) : (4Ld). Substitute Ld to get a pure number ratio.

Step-by-Step Solution:Ld = (4/3) Lc from 3Ld = 4Lc.Vc : Vd = 5Lc : 4Ld = 5Lc : 4*(4/3)Lc = 5 : 16/3 = 15 : 16.

Verification / Alternative check:Pick Lc = 3 and one time unit; then Ld = 4. Cat covers 5*3 = 15 units, dog covers 4*4 = 16 units ⇒ ratio 15 : 16.

Why Other Options Are Wrong:

• 11 : 15 and 15 : 11 ignore the stride-length relation.
• 16 : 15 inverts the correct order.

Common Pitfalls:

• Multiplying or dividing the frequency and length ratios inconsistently.
• Confusing “3 dog leaps = 4 cat leaps” with the reverse.

Final Answer:15 : 16