A locomotive engine without wagons can go 24 miles an hour and its speed is diminished as the square root of the number of wagons attached with 4 wagons its speed is 20 miles an hour. Find the maximum number of wagons with which the engine can move.

Explanation

Let the speed diminished by m mile / hour and the number of wagons =n .
As per question , m `prop sqrt(n) or , m=ksqrt(n) ………(1) ` (when k `ne` 0= variation constant)
Now , if 4 wagons be attached with the engine, its speed diminishes by
(24-20) mile/hour =4 mile /hour.
`therefore` from (1) we get , 4=k.` sqrt(4) or, 2k =4or, k=2`
`therefore` (1) cecomes , m `2sqrt(n) .....(2)`
Putting m =24 in (2) we get , 24 =`2sqrt(n)`
`rArr sqrt(n) =12 rArr n=(12)^2 =144`.
`therefore the engine will be speedless if 144 wagons are attached with it.
Hence the required maximum number of wagons =144-p1=143 .