Question

A passenger train takes one hour less for a journey of 150 km if its speed is increased by
5 km/hr from the usual speed. Find the usual speed of the train.

Answer 1

The usual speed of the train is 25 km/hr.

Step-by-step explanation:

Consider X be the usual speed of the passenger train.

Distance covered = 150 km

Time taken = Distance / Speed

$\text{Hence the time taken with normal speed} = \frac{ 150}{\text{X}}$

        $\text{The time taken with normal speed} = \frac{ 150}{\text{X}+5}$

The difference between both the time periods is 1 hour.

$\frac{ 150}{\text{X}} - \frac{ 150}{\text{X}+5} = 1$

$150[\frac{ 1}{\text{X}} - \frac{ 1}{\text{X}+5}] = 1$

$150[\frac{\text{X}+5 -\text{X}}{\text{X(X}+5)}] = 1$

$150[\frac{\text{X}+5 -\text{X}}{\text{X}^2+5}] = 1$

150 × 5 = X² + 5X

750 = X² + 5X

X² + 5X - 750 = 0

(Splitting 5x as (30X -25X) considering 30 and -25 are factors of -750)

X²+ 30X- 25X - 750=0

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

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

X+30 = 0 ,hence X= -30

X-25 = 0,hence X=25

As the time factor cannot be measured in negative the X with the positive value 25 is taken.

Hence the usual speed of the train is 25 km/hr.

To Learn More.....

1. A train takes 2 hour less 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.

brainly.in/question/5190243

2. An express train takes 30 minutes less for a journey of 440 km, if its usual speed is increased by 8 km/hr. Find its usual speed

brainly.in/question/2325824