1.

A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed were 5km/hr is more.find the orginal speed of train

Answer»

Let the uniform/original speed be x km/hr.

Then according to question,

360/x = 360/x+5 + 48/60 

We divide 48 by 60 in order to convert it into hr from min.

360/x - 360/x+5 = 48/60

360(x+5) - 360(x) / x(x-5) = 4/5

5(360 x - 360 x + 1800) = 4 (x² - 5 x)

5(1800) = 4(x² - 5 x)

9000 = 4 x² - 20 x

⇒ 4 x² - 20 x - 9000

(÷4)

⇒ x² - 5 x - 2250

⇒ x² - 50 x + 45 x - 2250

⇒ x(x-50) + 45(x-50)

⇒ (x+45)(x-50)

Then x = -45 km/hr, 50 km/hr

As speed cannot be negative.

Hence original/uniform speed is 50 km/hr.
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