Question

The reduction in speed of a railway engine is directly proportional to the square root of the number of compartments attached to it. With no compartments attached to the engine, the speed is 42 km/h. With 9 compartments attached to the engine, the speed is 24 km/h. What are the maximum number of compartments that can be attached to the engine?

• A. 49
• B. 48
• C. 46
• D. 47

Hint:

When dealing with proportional relationships, be sure to apply the square root function correctly and solve for unknowns.

Answer 1

The Correct Option is B

Let \( k \) be the constant of proportionality, and let the speed when there are \( n \) compartments attached be \( v \). From the relation, we have: \[ v = 42 - k\sqrt{n} \] Using the given values: \[ 24 = 42 - k\sqrt{9} \quad \Rightarrow \quad k = \frac{18}{3} = 6 \] Now, substituting \( k = 6 \) into the equation for \( v = 0 \), we get the maximum number of compartments as 48.