Q4 of 83 Page 90

A car takes 1 hour less to cover a distance of 200 km if its speed is increased by 10 km/hr, than its usual speed. What is the usual speed of the car?

Let the usual speed be – x km/hr and time taken to cover 200 km be – t.

⇒



Now, when the car speed will be increased by the 10 km/hr, then the speed will become – (x + 10) 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




⇒ 200x + 2000 – 200x = x2 + 10x


⇒ x2 + 10x – 2000 = 0


⇒ x2 + (50 – 40)x – 2000 = 0


⇒ x2 + 50x – 40x – 2000 = 0


⇒ x(x + 50) – 40(x + 50) = 0


⇒ (x + 50)(x – 40) = 0


⇒ x = – 50 or x = 40


And speed cannot be negative.


⇒ x = 40 km/hr.


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