The speed of a railway engine is 42 kmph 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 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is	Choose the correct answer.
A) 47
B) 48
C) 49
D) 50
E) 51
Explanation :   Let S = speed, and N = number of compartments, then   =&gt; S = 42 - k * √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   =&gt; 24 = 42 - k*√9 = 42 - 3k.   =&gt; 3k = 18.   =&gt; k = 6.   Now, we need to know: what value of N makes S go to zero?   =&gt; 0 = 42 - 6*√N   =&gt; 6*√N = 42   =&gt; √N= 7   =&gt; n = 7(2) = 49.   With 49 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars.   Thus, 48 is the maximum number of cars the engine can pull and still move.   Answer : 48
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The speed of a railway engine is 42 kmph 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 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is