Question

The distance between mumbai and pune is 192 km travelling by deccan queen it takes 48 minutes less than another train calculate the speed of deccan queen if the speed of two trains differ by 20 km/ hr no links please Answer accordingly

Answer 1

Let Speed of deccan queen = x km/h
Speed of other train = (x - 20) km/h

48 min = 48/60 hours = 0.8 hours

Difference in time = 192/(x-20) - 192/x = 0.8
This simplifies to:
3840 = 0.8x² -16x
x² - 20x - 4800 = 0; This is a quadratic equation
x² - 80x + 60x - 4800 = 0
x(x - 80) + 60(x - 80) = 0
(x - 80) (x + 60) = 0
Either x - 80 = 0 ⇒ x = 80
Or x + 60 = 0 ⇒ x = -60

Take x = 80

∴ The speed of the deccan queen = 80 km/h

Answer 2

Solution:-

Let the speed of another train be 'x' km/hr
So, the speed of Deccan Queen will be (x + 20) km/hr
Deccan Queen takes 48 minutes less than the another train = 48/60
= 4/5 hour
now, according to the question 
⇒ (192/x) - (192/x+20) = 4/5
⇒ (192x + 3840 - 192x)/(x)(x+20) = 4/5
⇒ (4x² + 80x - 19200 = 0) ÷ 4
⇒ x² + 20x - 4800 = 0
⇒ x² + 80x - 60x - 4800 = 0
⇒ x(x + 80) - 60(x + 80) = 0
⇒ (x + 80) (x - 60) = 0
⇒ x = - 80 or x = 60
Speed cannot be negative. So, x = 60 is correct.
So, the speed of another train is 60 km/hr and speed of Deccan Queen is   60 + 20 = 80 km/hr
Answer.