Question

Answer with step by step explanation​

Answer 1

Answer:

speed of passenger train= x =42 km/h

speed of express train= x+14= 56km/h

Time taken by passenger train= y = 4hrs

Time taken by express train= y-1= 3 hrs

Step-by-step explanation:

let the speed of passenger train be 'x' km/h

and time taken be 'y' hrs

=》 speed of express train = (x+14) km/h

=》 time taken by express train=( y-1) hrs

• Distance is same for both trains i.e. 168 km

☆ distance= speed×time

• for passenger train,

=》168 = x × y

=》168 = xy ----------(1)

=》(168)/y= x----------(2)

• for express train,

=》168 = (x+14) × (y-1)

=》168= (x+14)×y - (x+14)×1

=》168= xy+14y - x -14

=》xy = xy+14y - x -14_______(from(1))

=》xy-xy= 14y - x -14

=》0=14y - x -14

=》x-14y+14=0_________( sign change)

=》(168)/y-14y+14=0________(from (2))

=》(168-14y²+14y)/y=0

=》168-14y²+14y=0×y

=》168-14y²+14y=0

•Now solve tjis quadratic equation

=》0=14y²-14y-168_____(sign change)

=》0= y² -y - 12_______(divide by 14)

=》0= y² -4y+3y -12______( factorization)

=》0=y(y-4) +3(y-4)

=》0= (y-4)(y+3)

=》0= y-4 OR 0= y+3

=》y= 4 OR y=-3

• since, time cannot be negative,

• y=4

(putting value of y in (2))

=》 x=168/4

=》 x= 42

• thus,

speed of passenger train= x =42 km/h

speed of express train= x+14= 56km/h

Time taken by passenger train= y = 4hrs

Time taken by express train= y-1= 3 hrs

Hope you got it