## Problem Of The Week 47

**The speed of the engine of a train is 150 km/hr. By connecting coaches to the engine its speed decreases. The decrease in speed is given by the function d=x^2+3x-2 (km/hr), where x is the number of coaches connected. Find the minimum speed ( in km/hr) with which the train can run?**

**1) 1**

**2 11**

**3) 22**

**4) 33**

**5) None of these **

option 3

22

max number of coaches =10

did by trial and error.

is there a better way of doing this , instead of just trial and error??

qwertyOctober 8, 2008 at 12:35 pm

yupp there is

outtimedOctober 8, 2008 at 12:38 pm

can u please share that method .

qwertyOctober 8, 2008 at 12:52 pm

let others try at least, after that if no one gets it, i will post the solution

outtimedOctober 8, 2008 at 1:24 pm

for the egine to push the train the speed should be greater than 0…

Final speed of train= Speed of engine- decrease in speed.

At number of couches= 11 the decreease in speed = 121+33-2=152KMPH

this is not possible, decrease cannot be greater than 150…

so the number of Coachs has to be 10..with 10 d= 128KMPH

speed of train, with which it can run= 150-128=22…

Is this approach fine???

AnkajOctober 8, 2008 at 3:37 pm

x^2+3x-2<150 is the limiting case

solving we get

x^2+3x-152=0

x=(-3+-sqrt(617)/2

so x comes approx 11

so x should be less than 11

so x=10

put x=10 we get 128

so speed ia 150-128-122

outtimedOctober 9, 2008 at 6:09 am