Page 16 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

Solution: Let the speed of the train is x km/h. Then,

Time taken to cover the distance of 360km = 360 hours.
x

If the speed of the train is increased by 5 km/h. Then,

360
Time taken to cover the same distance = ( ) h
x+5

According to the question, 360 - 360 =1
x x+5

360 (x+5)-360x
⇒ =1⇒360x+1800-360x=x²+5x
x(x+5)

⇒x²+5x-1800=0 ⇒x²+45x-40x-1800=0

⇒x(x+45)- 40 (x+45)= 0 ⇒(x+45)(x-40)= 0

⇒x= -45 or x=40

The speed can not be negative.

So, the speed of the train is 40 km/h.

3
Example 6: Two water taps together can fill a taken in 9 hours. The
8
tap with larger diameter takes 10 hours less than smaller one to fill

the tank. Determine the time in which each tap can separately fill the

tank.

Solution: Let tap of larger diameter takes x hours in filling the tank.

So, the tap of smaller diameter will take (x + 10) hours to fill the tank.

∴ The portion of tank filled by the larger tap in one hour = 1/x, the

portion of tank filled by the smaller tap in one hour = 1
x+10
And portion of tank filled by both the smaller and the larger tap in one

1
hour = = 8
9 3 75
8

1 1 8
∴ + =
x x+10 75

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