Question

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

Answer 1

Answer:

25 km/h

Step-by-step explanation:

Define x:

Let the usual speed be x km/h

Find the usual time needed:

Time = Distance ÷ Speed

Time = 300/x hours

Find the time needed if the speed is increased:

Time = Distance ÷ Speed

Time = 300/(x + 5) hours

Solve x:

The difference in time is 2 hours

300/x - 300/(x + 5) = 2

300(x + 5) - 300x = 2x(x + 5)

300x + 1500 - 300x = 2x² + 10x

2x² + 10x - 1500 = 0

x² + 5x - 750 = 0

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

x = 25 or x = - 30 (rejected, since speed cannot be negative)

Answer: The speed of the train is 25 km/h

Answer 2

Answer:

Let the usual speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the usual speed of the train is 25 km / hr .