Question

The speed of a railway engine is 42 km per hour when no compartment is attached and the reduction in speed is directly proportional to the square root of the number of compartment attached. If the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , what is the maximum number of compartments that can be carried by engine ?

Answer 1

Let Speed is the funcion of K1, K2 and n. K1 and K2 are constant and n is the no. of compartment.
Speed varies as,
S = K1 - K2(n) ^ 1/2
S= 42 when n = 0 and K1 = 42
S = 24 when n = 9, So K2 = 6
Now, S become
S = 42 - 6(n) ^ 1/2 it must be > 0 (always). So, n should be maximum which is less than 49, hence n = 48.