Different speeds: A four times faster than B Inlet A is four times as fast as inlet B. If A alone fills the tank in 15 minutes, how long will both together take to fill it?

Introduction / Context:
Relative-speed statements like “A is four times faster than B” define a rate ratio. Convert the statement into individual rates and then add the rates to get the joint time.

Given Data / Assumptions:

• A alone: 15 min ⇒ rate(A) = 1/15 per min.
• A is 4 times B ⇒ rate(B) = rate(A) / 4 = 1/60 per min.
• Tank initially empty; both start together.

Concept / Approach:
Total rate = rate(A) + rate(B). Time = 1 / total rate.

Step-by-Step Solution:

Verification / Alternative check:
In 12 min, A adds 12/15 = 4/5; B adds 12/60 = 1/5; total 1 tank.

Why Other Options Are Wrong:
10, 15, 14 contradict the combined rate 1/12.

Common Pitfalls:
Interpreting “4 times faster” as “A’s time is one quarter,” which is only true for rates, not times unless converted carefully.

Final Answer:
12 min