Question

* 3. If the usual uniform speed of a train is
increased by 5 km/h, it takes 48 minutes
less than the usual time to cover a distance
of 360 km. Find the usual uniform speed of
the train.​

Answer 1

Given :

• uniform speed of a train is increased by 5 km/h
• it takes 48 minutes less than the usual time
• cover a distance of 360 km.

To find :

• usual uniform speed of the train.

Solution:

Let initial speed of the train be x km/hr,

New speed is (x + 5) km/hr.

time to distance cover 350 km = distance/speed= 360/x hours

New time after increasing speed 360/x + 5 hours .... from given condition

360/x + 5 = 360/x - 48/60 (48 min = 48/60 hrs)

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

1/x - 1/x + 5 = 48/60 x 360 (Dividing both sides by 360)

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

5/x² + 5x 1/5 x 90

5/x² + 5x 1/450

x² + 5x = 2250

x² + 5x - 2250 =0

x² + 50x - 45x - 2250 = 0

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

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

x + 50 = 0 or x - 45 = 0

x = -50 or = 45

But speed is never negative x ≠ -50

x = 45

=> Initial speed of the train is 45 km/hr.