The Lucknow-Indore Express without its rake can go 24 km an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagon attached. If it is known that with four wagons its speed is 20 km/h, the greatest number of wagons with which the engine can just move is

let, x=24 kmph
y=20 kmph
N=(x^2/x-y)-1
=143

Speed = $45 - k sqrt{n}$ where n is the number of wagons

Speed with 9 wagons = $45 - k sqrt{9}$
$45 - k sqrt{9}$ = 30
45 - 3k = 30
3k = 15
k = 5

i.e., speed = $45 - 5 sqrt{n}$

Consider the case when the speed is zero
$45 - 5 sqrt{n} = 0$
$ 5 sqrt{n}= 45$
$ sqrt{n}= 9$
n = 81
This means, when the number of wagons = 81, speed = 0

i.e., when the number of wagons = 80, the train can just move

another way to solve the problem please