The speed of a railway engine is 63 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:  Select the correct option.
A) 19  B) 18  C) 16  D) 17  E) 23

Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached does reduction mean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 63 - k * sqrt ( n ) where k is a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 63 - k * sqrt ( 9 ) = 63 - 3 k k = 13 now , we need to know : what value of n makes s go to zero ? 0 = 63 - 13 * sqrt ( n ) 13 * sqrt ( n ) = 63 n = 23 with 24 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 23 is the maximum number of cars the engine can pull and still move . e
Answer: E