Answer with step by step explanation
Answers
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