The passenger train takes two 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 more the train?
Answers
Answer:
Step-by-step explanation:
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
\u00a0 \u00a0 \u00a0 \u00a0A\/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 ]
\u00a0\u21d2 240\/x - \u00a0240\/(x +20) = 2 \u00a0[ putting equation (1) in equation (2); ]
\u21d2 240 [ (x + 20 - x)\/x(x +20) ] = 2
\u21d2 120 [ 20\/(x\u00b2 + 20x) ] = 1
\u21d2 120 \u00d7 20 = x\u00b2 + 20x
\u21d2 x\u00b2 + 20x - 2400 = 0
\u21d2 x\u00b2 + 60x - 40x -2400 = 0
\u21d2 x(x + 60) -40(x + 60) = 0
\u21d2 (x + 60)(x - 40) = 0
\u21d2 x = 40 and -60 but speed can\u2019t be negative so, x \u2260 -60 km\/h
Hence, speed of the passenger train is 40km\/h
And speed of the express train is 60km\/h