Math, asked by varsha323, 1 year ago

consider two trains a and b such that a takes t hours to cover stretch of 200 km. now train b which is 25 kilometre per hour faster than a takes 24 minutes less than a. find the speed of the train a and b.​

Answers

Answered by arsalan010392
41

Answer:

Speed of Train A = x = 100 kmph

Speed of Train B = x +25 = 125 kmph

Step-by-step explanation:

Given :  Two trains A and B covers 200 km. Speed to train B is 25kmph more than speed of train A.

Also time taken by train A to cover 200 km is 't' hrs and by train B is 24 minutes less than train A

To find : Speed of train A and speed of train B

Consider speed of train A to be 'x' kmph

Therefore, speed of train B = ( x + 25 ) kmph

Time taken by train A to cover 200 km is 't' hrs,

i.e t = ( 200 / x)    hrs    ------        (i) [Time = Distance/Speed]

Therefore time taken by train B = [ t - ( 24 / 60 ) ] hrs  -------(ii)  [ 24 min =( 24 / 60 ) hrs ]

Total distance travelled = 200 kmph

Time taken by train B to cover 200 km = [ 200 / ( x + 25 ) ]  ---- (iii)

Equating time taken by train B to cover 200 km (equation (ii) & (iii)]

t - ( 24 / 60 ) = [ 200 / ( x + 25 ) ]

t - ( 2 / 5 ) = [ 200 / ( x+25 ) ] ------- (iv)

Putting the value of t from equation (i) into (iv)

we have,

( 200 / x  ) - ( 2 / 5 ) =  [ 200 / (  x + 25 ) ]

( 200 / x ) - [ 200 / ( x + 25 ) ] = ( 2 / 5 )

[ 200 ( x + 25 ) - 200 ( x ) ] / [ x ( x + 25 ) ]  = ( 2 / 5 )

[ 200x + 5000 - 200x ] / [ x ( x + 25 ) ]

5000 / [ x ( x + 25 ) ] = ( 2 / 5 )

( 5000 * 5 ) / 2 = [ x ( x + 25 ) ]

x ( x + 25 ) = 12500

x^2 + 25x = 12500

x^2 + 25x - 12500 = 0

Solving above quadratic equation

x^2 + 125x - 100x - 12500 = 0

x ( x + 125) -100 ( x + 125 ) = 0

( x +125 ) ( x - 100 ) = 0

x  + 125 = 0 or x - 100 = 0

x = -125 or x = 100

Since x is speed and it cannot be negative

Therefore true value of x = 100 kmph

Speed of Train A = x = 100 kmph

Speed of Train B = x + 25 = 125 kmph

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