Question

(ii) If the speed of a car is decreased by 8 km/h, it takes 1 hour more to cover a
distance of 240 km. Find the original speed of the car.​

Answer 1

Answer:

Let the speed of car be xkmph

Let it takes Time t hrs to cover the distance of 240km

⟹xt=240⋯(1)

speed is decreased by 8⟹x−8

Time is increased by 1⟹t+1

it covers the same distance so (x−8)(t+1)=240

xt+x−8t−8=240

From (1)⟹x−8t−8=0

x=8t+8

Put it in (1)⟹(8t+8)(t)=240

t

2

+t−30=0

t

2

+6t−5t−30=0

t(t+6)−5(t+6)=0

(t−5)(t+6)=0

t=5,−6

Time cannot be negative so t=5

Put it in (1)

⟹x(5)=240⟹x=12kmph

Step-by-step explanation:

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Answer 2

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

 Time taken to cover 240 km:

⇒ 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