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
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