Question

A train takes 2 hours les for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. find the usual speed of the train

Answer 1

let usual speed of train = x km/hr
total distance = 300 km
so time taken = 300 / x  hours ----(i)

new speed of train = x + 5 km/hr
now time taken = 300 / (x+5) ----(ii)

according to given condition 
 300/x  -  300/(x+5) = 2 
 (300x + 1500 - 300x) / [x(x+5)] = 2
 1500 = 2x^2 + 10x
 x^2 + 5x - 750 =0
x^2 + 30x - 25x -750 = 0
x(x + 30) -25(x + 30)
(x - 25) (x + 30) = 0
so x = 25

that's why usual speed of train = 25 km/hr


i hope it will help you
regards

Answer 2

Answer:

Given: Total distance of a journey = 150 km

Let the usual speed of the train be x km/h  and the increased  speed of the train is (x + 5) km)h.

Time taken by the train with usual speed to cover 150 km= 150/x hrs

Time taken by the train with increased speed to cover 150 km= 150/(x + 5) hrs  

[ Time = Distance/speed]

150/(x + 5) = 150/ x   - 1

150/ x -  150/(x + 5)  = 1

[150(x + 5) - 150x] /(x(x + 5) = 1

[By taking LCM]

150x + 750 - 150x /(x² + 5x) = 1

750 / x² + 5x = 1

(x² + 5x ) = 750

x² + 5x - 750 = 0

x² - 25x + 30x - 750 = 0

[By middle term splitting]

x(x - 25) + 30 ( x - 25) = 0

(x - 25) (x + 30) = 0

x = 25 or x = - 30  

Since, speed can't be negative, so x = - 30  

Therefore,  usual speed of the train be = x = 25 km/h