Question

a train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. find the usual speed of the train. NEED AN EXPLANATION Too...

Answer 1

◀  HEY THERE!◀

◀ Question: ◀

A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train ?

◀  Method of Solution: ◀

Let to be actual Speed of the train = x km/hr

◀ Given: ◀

Total Distance covered by train = 300 kilometers.→

•°• Time Taken = 300/x.     -----(1)

Now, According to the Question!!→

Speed increase = x+5

•°•. ⇒  Speed = x+5/300.  ---------(2)

From Equation (1) and (2)

⇒  300/x - 300/x+5 = 2

⇒ 300x + 1500-300x /x(x+5) = 2

⇒ 1500/x²+5x = 2

⇒ 1500 = 2x²+10x

•°• 2x²+10x -1500 = 0

⇒  2(x²+5x-750) = 0

•°• x²+5x -750 = 0

Solving by Splitting Method!→

⇒ x²+30x-25x -750 = 0

⇒ x(x+30) -25(x+30) = 0

•°• (x+30)(x-25)=0

x =-30 or 25

Hence, x = 25 km/hr

◀ Conclusion: ◀

→  Actual Speed of the train = 25 km/hr→

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 .