Question

Train A takes 45 minutes more than train B to travel a distance of 450 km. Due to engine trouble speed of train B falls by a quarter, so it takes 30
minutes more than Train A to complete the same journey. What is the speed of Train A (in km/hr)​

Answer 1

Answer:

Required speed of train A is 100 km / hr.

Step-by-step explanation:

Let the time taken to complete the whole journey by train B be a hours.

So, time taken by train A to be complete the journey should be [ a + ( 45 x 1 / 60 ) ] hours i.e. ( a + 3 / 4 ) hours.

Thus,

= > Speed of train A = ( Distance / time )

= > Speed of train A = 450 / ( a + 3 / 4 ) km / hr

According to the question :

Due to engine trouble speed of train B falls by a quarter, so it takes 30

minutes more than train A to complete the same journey.

Thus,

= > Speed of train B due to trouble = 450 / a km / hr - 1 / 4 of 450 / a km / hr

= > Speed of train B due to trouble = ( 450 / a - 1 / 4 of 450 / a ) km / hr

= > Speed of train B due to trouble = 675 / 2a km / hr ... ( 1 )

Given, due to trouble in engine, now,

= > Time taken by train B = time taken by train A + 30 minutes

= > Time taken by train B due to trouble = a + 3 / 4 + ( 30 x 1 / 60 ) hr

= > Time taken by train B due to trouble = a + 3 / 4 + 1 / 2 hr

= > Time taken by train B due to trouble = ( a + 5 / 4 ) hr

From this, speed of train B after trouble = 450 / ( a + 5 / 4 ) ....( 2 )

Comparing ( 1 ) & ( 2 ) :

= > 675 / 2a = 450 / ( a + 5 / 4 )

= > 675 / 2a = ( 450 x 4 ) / ( 4a + 5 )

= > 675( 4a + 5 ) = 450 x 4 x 2a

= > 2700a + 3375 = 3600a

= > 3375 = 900a

= > 15 / 4 = a

Hence the speed of train A is 450 / ( 15 / 4 + 3 / 4 ) km / hr = 450 / ( 18 / 4 ) km / hr = 100 km / hr.

Hence the required speed of train A is 100 km / hr.

Answer 2

Solution :-

Let speed of A be A km/hr.

Let speed of B be B km/hr.

According to the question,

⇒ 450 / A – 450 / B = 45 / 60

⇒ (1 / A – 1 / B) = 1 / 600 .....(1)

And

⇒ 450 / (3B / 4) – 450 / A = 30 / 60

⇒ 4 / 3B – 1 / A = 1 / 900 .....(2)

Adding both the equations,

⇒ 4 / 3B – 1 / B = 1 / 600 + 1 / 900

⇒ 1 / 3B = 5 / 1800

⇒ B = 120 km/hr

∴ Speed of B = 120 km/hr

Putting this value in equation 1,

⇒ 1 / A = 1 / 600 + 1 / 120

⇒ 1 / A = 6 / 600

⇒ A = 100 km/hr

∴ Speed of A = 100 km/hr