Question

A car travels a distance of 900 km with a certain speed. Of after travelling, the speed is increased by 15 km/h, time required to travel 900 km is reduces by 1and half hours. find the original speed of car.

Answer 1

HELLO DEAR,

total distance=900km

let the usual speed be X km/h

time=distance/speed

time TAKEN to cover the distance in 900 km

=> 900/x

-------------------------and-------------------------

after traveling half the distance=900/2
=> 450km
and the increase of speed is 15km

then time taken to cover with speed (15+X)
=> 450/(x+15)

$\frac{450}{x} = \frac{450}{x + 15} = 1\frac{1}{2} = \frac{3}{2} \\ = > \frac{450}{x} - \frac{450}{x + 15} = \frac{3}{2} \\ = > 450( \frac{x + 15 - x}{x(x + 15)}) = \frac{3}{2} \\ = >450( \frac{15}{ {x}^{2} + 15x } )= \frac{3}{2 } \\ = > \frac{15}{ {x}^{2} + 15x} = \frac{3}{2 \times 450} \\ = \frac{5}{ {x}^{2} + 15x} = \frac{1}{2 \times 450} \\ = > 4500 = {x}^{2} + 15x \\ = > {x}^{2} + 15x - 4500 = 0 \\ = > {x}^{2} + 75x - 60x - 4500 = 0 \\ = > x(x + 75) - 60(x + 75) = 0 \\ = > (x - 60)(x + 75) = 0 \\ = > x = - 75 \\ \\................... or.................... \\ x = 60 \frac{km}{hr}$

I HOPE ITS HELP YOU DEAR,
THANKS