Question

an Express train takes 1 hour less than a passenger train to travel 132 kilometre if the average speed of the express is 11 km per hour more than that of passenger train find the average speed of two trains

Answer 1

Hey

Here is your answer,

let the usual speed of train be x km/hr,

Then the increased speed of the train is = (x + 11) km/hr

Time taken by the passenger train to cover 132 km = 132/x hr

Time taken by the express train to cover 132 km = 132/(x + 11)hr

Therefore,

132x–132(x+11)=1
132/x–132/(x+11)=1
132(x+11)–132x(x+11)=1
132(x+11)–132x/x(x+11)=1
132x+1452–132x/x2+11x=1
132x+1452–132x/x2+11x=1

1452 = x2 + 11x
x2 + 11x – 1452 = 0
x2 – 33x + 44x – 1452 = 0
x(x – 33) + 44(x – 33) = 0
(x – 33)(x + 44) = 0

x = 33 or x = – 44

Since, speed of train can never be negative

Therefore, speed of passenger train = 33 km/hr.

And speed of express train, = (x + 11) = (33 + 11) = 44 km/hr.Here

Hope it helps you!