A passenger train takes 2 hours more than express train to travel a distance of 240km. The speed of the express train is more than that of passenger train by 20 km/h . Find the speed of both 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
Let the speed of passenger train be = x
Speed of express train = x + 20
Distance to be travelled by both trains = 240 km
Time = Distance/Speed
Time taken by the express train = 240/(x + 20)
Time taken by passenger train = 240/x
Also, given that time taken by passenger train = time taken by express train + 2 hours
=> 240/x = 240/(x + 20) + 2
=> 240/x = (240 + 2x + 40)/(x + 20)
=> 240/x = (280 + 2x)/(x + 20)
=> 240(x + 20) = x(280 + 2x)
=> 240x + 4800 = 280x + 2x^2
=> 2x^2 + 40x - 4800 = 0
=> x^2 + 20x - 2400 = 0
=> x^2 - 40x + 60x - 2400 = 0
=> x(x - 40) + 60(x - 40) = 0
=> (x + 60)(x - 40) = 0
=> x = 40, -60
Since speed can't be negative:-