When there is a decrease of 5 km/hr in the usual uniform speed of a goods train, due to track repair work going on it takes 4 hours more than the usual time for travelling the distance of 400 km. Find the usual speed of the train.
Let the usual speed be – x km/hr and time taken to cover 400 km be – t.
Now, when the car speed will be decreased by the 5 km/hr, then the speed will become – (x – 5) km/hr.
Now, let the time taken now be T
But given that car took 4 hr. more to cover 200 km by new speed.
⇒ T = t + 4
⇒ 400x + 2000 – 400x = 4x2 – 20x
⇒ 4x2 – 20x – 2000 = 0
Dividing whole equation by 4, we get –
⇒ x2 – 5x – 500 = 0
⇒ x2 – (25 – 20)x – 2000 = 0
⇒ x2 – 25x + 20x – 2000 = 0
⇒ x(x – 25) + 20(x – 25) = 0
⇒ (x – 25)(x + 20) = 0
⇒ x = 25 or x = – 20
And speed cannot be negative.
⇒ x = 25 km/hr.
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