The distance between two places is 1200 km. To cover this distance, a person X takes 5 hours lesser than another person Y, whose average speed is 40 km/h lesser than that of X. The time taken by Y to complete the travel is:

Let the time taken by Y be t hours.
Then, the time taken by X is (t−5) hours.

Distance = 1200 km.
Speed of Y (S
Y
​
) =
t
1200
​

Speed of X (S
X
​
) =
t−5
1200
​


According to the question, the speed of Y is 40 km/h lesser than X:

S
X
​
−S
Y
​
=40
t−5
1200
​
−
t
1200
​
=40
Dividing the entire equation by 40:

t−5
30
​
−
t
30
​
=1
30(
t(t−5)
t−(t−5)
​
)=1
t(t−5)
30×5
​
=1
150=t(t−5)
t
2
−5t−150=0
Factoring the quadratic equation:

t
2
−15t+10t−150=0
(t−15)(t+10)=0
Since time cannot be negative, t=15 hours.