Q8 of 83 Page 90

The difference of the speed of a faster car and a slower car is 20 km/hr. If the slower car takes 1 hour more than the faster car to travel a distance of 400 km, find speed of both the cars.

Let the usual speed be – x km/hr and time taken to cover 400 km be – t.

⇒


Now, when the car speed will be increased by the 20km/hr, then the speed will become – (x + 20) km/hr.


Now, let the time taken now be T



But given that car took 1 hr. less to cover 200 km by new speed.


⇒ t – T = 1




⇒ 400x + 8000 – 400x = x2 + 20x


⇒ x2 + 20x – 8000 = 0


⇒ x2 + (100 – 80)x – 2000 = 0


⇒ x2 + 100x – 80x – 8000 = 0


⇒ x(x + 100) – 80(x + 100) = 0


⇒ (x + 100)(x – 80) = 0


⇒ x = – 1000 or x = 80


And speed cannot be negative.


⇒ x = 80 km/hr.


And speed of faster car = 100 km/hr.


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