Question

If speed of the car is decreased by 8 kméh, it take
1 hour more to cover a distance of 240 km. find the
original speed of the car
cat.​

Answer 1

Let the original velocity of the car be 'x' kmph.

 Time taken to cover 240 km:

⇒ speed = distance/time

⇒ x = 240/time

⇒ time = 240/x          

When speed is decreased by 8: time increases by 1,

⇒ (x - 8) = 240(time + 1)

⇒ time + 1 = 240/(x - 8)

⇒ (240/x) + 1 = 240/(x - 8)

⇒ (240 + x)/x = 240/(x - 8)

⇒ (240 + x)(x - 8) = 240x

⇒ 240x - 1920 + x² - 8x = 240x

⇒ x² - 8x - 1920 = 0

⇒ x² - 48x + 40x - 1920 = 0

⇒ (x + 40)(x - 48) = 0

   x = 48,    ∴ speed of the car is 48 kmph

Answer 2

Given :-

If speed of the car is decreased by 8 km/h, it take  1 hour more to cover a distance of 240 km

To Find :-

Original speed of car

Solution :-

Let,

Time = y

Speed = x

When speed decreased by 8

$\sf x-8$

When time increased by 1 hr.

$\sf y+1$

xy = 240

Now,

Distance covered is 240 km/h

$\sf (x-8)(y+1) = 240$

$\sf xy +x-8(y)-8=240$

$\sf x-8y-8=0$

$\sf x = 8y+8$

$\sf y^2 +y-30=0$

$\sf y^2+(6y-5y)-30=0$

$\sf y^2+6y-5y-30=0$

$\sf y(y+6) - 5(y+6)$

$\sf (y-5) or (y+4)$

Either

y = 5

or

y =-4

Time can't be negative

So,

y = 5

xy = 240

x(5) = 240

x = 240/5

x = 12