Question

A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speeds where 5 km per hour more. Find the original speed of the train

Answer 1

Answer:

45 km/hr

Step-by-step explanation:

Let the original speed of the train = x km/hr.

Given, Distance to be traveled = 360 km.

∴ Time = Distance/Speed.

So, Initial Speed = 360/x.

Increased Speed = (360/x + 5).

Given that It would have taken 48 minutes less to travel.

⇒ (360/x) - (360/x + 5) = 48/60

⇒ (90/x) - (90/x + 5) = 1/5

⇒ 90(x + 5) - 90(x) = x(x + 5)/5

⇒ 5[90x + 450] - 5(90x) = x² + 5x

⇒ 450x + 2250 - 450x = x² + 5x

⇒ 2250 = x² + 5x

⇒ x² + 5x - 2250 = 0

⇒ x² + 50x - 45x - 2250 = 0

⇒ x(x + 50) - 45(x + 50) = 0

⇒ (x - 45)(x + 50) = 0

⇒ x = 45, -50{Since Speed cannot be negative, So x≠ 50}

⇒ x = 45.

Therefore, Original speed of the train = 45 km/hr.

Hope it helps!

Answer 2

Step-by-step explanation:

let the original speed of the train be X km/h

Increased speed=X+5

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

90/X -90/X+5=1/5

90(X+5) -90(X)/X2+5X=1/5

450X+2250-450X=X2+5X

X2+5X-2250=0

X2+50X-45X=0

X(X+50)-45(X+50)=0

(X+50) (X-45)=0

X=45km/h