Given:
Train
X takes 2 hours less than a train
Y Distance between two cities
192km Average speeds differ by
16km∕hr Formula Used:
Speed
= Distance
∕ Time
Calculation:
According to the question
X is faster train since it takes less time than
y to cover a fixed distance
Let the time taken by train
X be
xhr So, the time is taken by
Y be
(x+2)hr Now, According to the question
⇒−=16 ⇒−=1 From here, we can use the option to find directly the answer otherwise follow the given solution
⇒12(x+2)−12x=x(x+2) ⇒24=x2+2x ⇒x2+2x−24=0 ⇒x2+6x−4x−24=0 ⇒x(x+6)−4(x+6)=0 ⇒(x+6)(x−4)=0 ⇒x=−6 or x=4 We know that time can not be negative
So,
x=4 ∴ The time taken by the faster train to cover the distance is
4hr :