A dog makes 4 leaps in the same time a cat makes 5 leaps. The distance of 3 dog leaps equals the distance of 4 cat leaps. What is the ratio of their speeds (dog : cat)?

Introduction / Context:
Speed equals step frequency multiplied by step length. We are given a ratio of leaps per equal time and a relation between leap lengths. Combine them to get the speed ratio.

Given Data / Assumptions:

• Leaps per equal time: dog : cat = 4 : 5.
• 3 dog leaps = 4 cat leaps → L_d / L_c = 4/3.
• Uniform steps; no acceleration.

Concept / Approach:
If n is leaps per time and L is length per leap, then speed v = n * L. Hence v_d / v_c = (n_d * L_d) / (n_c * L_c).

Step-by-Step Solution:
n_d / n_c = 4/5.L_d / L_c = 4/3 (from 3L_d = 4L_c).v_d / v_c = (4/5) * (4/3) = 16/15 → 16 : 15.

Verification / Alternative check:
Scale leap counts over one minute and multiply by lengths to confirm the same ratio numerically.

Why Other Options Are Wrong:
Other ratios arise from inverting the frequency or length relations or mixing 3 and 4 incorrectly.

Common Pitfalls:
Using 3/4 instead of 4/3 for lengths; adding ratios rather than multiplying.

Final Answer:
16 : 15