Question

The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and cost $48 per hour at 16 miles per hour. The most economical speed if the fixed charges (i.e., salaries etc.) amount to $30 per hour is:

• A. \(10\)
• B. \(20\)
• C. \(30\)
• D. \(40\)

Hint:

Economic speed occurs when running cost equals fixed cost.

Answer 1

The Correct Option is B

Step 1: Fuel cost \(\propto v^2\Rightarrow\) cost \(=kv^2\).
Step 2: Given \(k=\dfrac{48}{16^2}=0.1875\).
Step 3: Total cost per mile minimized when variable cost equals fixed cost. \[ v=\sqrt{\frac{30}{0.1875}}=20 \]