Question

Q. 31( or)find the roots....
Plz answer quickly..

Answer 1



Secondary School

Math

8 points

A train travels 180km at a uniform speed. If the speed had been 9km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Let the speed of train be x km /h
Distance = 180 km
So, time = 180 / x
When speed is 9 km/h more, time taken = 180 / x+9 
According to the given information:
180 / x - 180 / x+9 = 1
180 (x+9-x) / x(x+9) = 1
180 * 9 = x(x+9)
1620 = x2 + 9x 
x2 + 9x - 1620 = 0
x2 + 45x - 36x - 1620 = 0 
x(x+45) - 36(x+45) = 0
(x-36)(x+45) = 0
x = 36 or -45
But x being speed cannot be negative.
So, x = 36
Hence, the speed of the train is 36km/h.

Answer 2

let the speed of the train is x

we know that Time= distance/speed

ATQ

$\frac{180}{x + 9} - \frac{180}{x} = 1 \\ 180( \frac{x - x - 9}{ {x}^{2} + 9x } ) = 1 \\ 180 \times 9 = {x}^{2} + 9x \\ 162 = {x}^{2} + 9x \\ {x}^{2} + 9x - 1620 = 0 \\ {x}^{2} + 45x - 36x - 1620 = 0 \\ x(x + 45) - 36(x + 45) = 0 \\ (x - 36)(x + 45) = 0 \\ x - 36 = 0 \\ x = 35$

speed of the train will be 35 km/hr.