A passenger train takes 2 hours more than an Express train to travel a distance of 240 km the speed of the express train is more than that of the passenger train by 20 km per hour find the speed of both the trains
Answers
Answer: speed of the passenger train is 40km/h
Speed of the express train is 60km/h
Step-by-step explanation: Let the speed of the passenger train is x km/h
Speed of the express train is y km/h
A/c to question,
Passenger train takes 2 hours more than an express train to travel a distance of 240km. Also the speed of the express train is more than that of the passenger train by 20km/h
e.g., x + 20 = y .............(1)
240/x = 240/y + 2 .........(2) [ time = distance/speed ]
⇒ 240/x - 240/(x +20) = 2 [ putting equation (1) in equation (2); ]
⇒ 240 [ (x + 20 - x)/x(x +20) ] = 2
⇒ 120 [ 20/(x² + 20x) ] = 1
⇒ 120 × 20 = x² + 20x
⇒ x² + 20x - 2400 = 0
⇒ x² + 60x - 40x -2400 = 0
⇒ x(x + 60) -40(x + 60) = 0
⇒ (x + 60)(x - 40) = 0
⇒ x = 40 and -60 but speed can’t be negative so, x ≠ -60 km/h
Hence, speed of the passenger train is 40km/h
And speed of the express train is 60km/h
Answer: speed of passenger train is equal to 40 km per hour and speed of Express train is equal to 60 km per hour
Step-by-step explanation:
let speed of passenger train be x kilometre per hour
Therefore according to given condition the speed of Express train will be 20 km per hour more than speed of passenger train which is equal to express 20 km per hour
We know that time is equal to distance/ speed
Therefore time required by Passenger train to cover the distance is equal to 240 / x
similarly time required to express train to cover the same distance is equal to 240 / X + 20
according to given condition passenger train requires 2 hours more than Express train to cover the distance
therefore time required by Passenger train - time required by express train = 2
240 / X - 240 / X + 20 = 2
240x + 4800 - 240x / x^2 + 20x = 2
4800 divided by X square + 20 x is equal to 2
x square + 20 X / 4800 = 1/2
x square + 20 x = 4800/2
x square + 20x = 2400
x square + 20x - 2400 =0
x square + 60 x - 40x - 2400 = 0
x (x + 60 ) - 40 (x+ 60) = 0
(x +60 ) ( x- 40) = 0
x+60 = 0 (which is not applicable )
or x - 40 = 0
therefore x is equal to 40
& x + 20 = 60
Therefore speeds of passenger train and Express train are 40 kilometre per hour and 60 km per hour respectively