Question

A train travels a distance of 480 km at a uniform speed. If the speed had
been 8 km/hr less, then it would have taken 3 hours more to cover the
same distance. Find the usual speed of the train.​

Answer 1

Answer:

40km/h

Step-by-step explanation:

as attached

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Answer 2

Answer:

Let the usual speed of the train be

x km/h

Reduced speed of the train

= (x – 8) km/h

Distance of journey = 480km

Time taken to reach destination at usual speed = 480 *h/x

Time taken to reach destination at reduced speed = 480*h/x-8

According to given question-

$\frac{480}{x - 8} = \frac{480}{x} + 3 \\ = > \frac {480}{x - 8} - \frac{480}{x} = 3 \\ \frac{480 \: x - 480x + 3840}{x(x - 8)} = 3 \\ \frac{3840}{x(x - 8)} = 3$

⇒ x2 – 8x = 1280

⇒ x2 – 8x – 1280 = 0

⇒ x2 – 40x + 32x – 1280 = 0

⇒ x(x – 40) + 32(x – 40) = 0

⇒ (x – 40)(x + 32) = 0

⇒ x = 40 or x = – 32

⇒ x = 40 (speed cannot be negative)

Hence the usual speed of the train is 40 km/h

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