plz give me answer fast
Answers
AnswEr
The correct option is
c) 40 km/hr
Given
- The total distance travelled by train is 360km
- If the speed of train is 5km/h more the journey takes 1hour less .
To Find
- The speed of the train
Solution
Let us consider the speed of the train be x km/h
We know that
speed = distance/time
⇒ x = 360/t _____(1)
and
⇒ x + 5 = 360/(t - 1)
⇒ x = 360/(t - 1) - 5
⇒ x ={360 - 5(t - 1)}/(t-1)_____(2)
Comparing (1) and (2) we have
⇒ 360/t =( 360 - 5t + 5)/(t - 1)
⇒ 360(t - 1) = t( 365 - 5t)
⇒360t - 360 = 365t - 5t²
⇒ -5t² + 5t + 360 = 0
⇒ 5t² - 5t - 360 = 0
⇒ 5(t² - t - 72) = 0
⇒ t² - t - 72 = 0
⇒ t² + 8t - 9t - 72 = 0
⇒ t(t + 8) - 9(t + 8) = 0
⇒ (t - 9)(t + 8)
Therefore ,
t - 9 = 0 or t + 8 = 0
⇒ t = 9 or⇒ t = -8
Since time can never be negative so t ≠ -8
Thus time taken is 9 hours
Since speed = distance/time
⇒ x = 360/9
⇒x = 40
The speed of the train is 40km/h
A train travels 360 km at a uniform speed .
If the speed had been 5 km/h more, it would have taken 1 hours less for the same journey . Find the speed of train ?
- Train have complete total distance in own journey = 360 km
- If train had been 5 km more, then its have take 1 hours less to complete same journey .
- Speed of train .
Let,
Again, A/C to question,
( If train had been 5 km more, then its have take 1 hours less to complete same journey . )
Here,
- speed (S) = S + 5 km/h
- time (t) = (t-1) h
Substitute value of S by equ(1)
Since,
Time be not negative
- t ≠ -8
So, Take t = 9
Keep value of t in equ(1),
This is required speed of train .
- Answer will be options number (C).