Cars A and B start 88 km apart and drive towards each other. Speed ratio A:B = 5:6, and B's speed is 90 km/h. After how long do they meet?

Introduction / Context:
Opposite-direction approach with a known ratio allows computation of the other speed and thus the relative approach rate.

Given Data / Assumptions:

• B = 90 km/h, A:B = 5:6 → A = 75 km/h.
• Initial separation = 88 km.

Concept / Approach:
Relative speed toward each other = A + B = 75 + 90 = 165 km/h. Time = distance / relative speed.

Step-by-Step Solution:
t = 88 / 165 h = 0.5333.. h = 32 minutes.

Verification / Alternative check:
Distance covered by A in 32 min: 75*(32/60) = 40 km; by B: 90*(32/60) = 48 km; total 88 km.

Why Other Options Are Wrong:
24, 26, 36 min correspond to relative speeds inconsistent with 165 km/h.

Common Pitfalls:
Using difference of speeds by mistake (used for same-direction problems).

Final Answer:
32 min