An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express trains is 11 km / hr more than that of the passenger train, find the average speeds of the two trains.
Answers
Answer:
SPEED OF PASSENGER TRAIN = 33 km/hr
SPEED OF EXPRESS TRAIN = 44km/hr
Step-by-step explanation:
let the average speed of the passenger train be x km/hr and the the average speed of the express train be (x+11) km/hr
Total Distance = 132 km
Time taken by passenger train = 132/x
Time taken by Express train = 132/(x+11)
According to the problem,
132/x - 132/(x+11)=1
on solving this, we get the below quadratic equation,
x^2 + 11x - 1452 = 0
By Factorisation,
x^2 + 44x - 33x - 1452 = 0
So, x= -44 or x= 33
speed cannot be negative,
so, x= 33
SPEED OF PASSENGER TRAIN = 33 km/hr
SPEED OF EXPRESS TRAIN = 44km/hr
hope this will help you
Average Speed of Two Trains = 37.7 km/Hr
Step-by-step explanation:
Let say speed of Passenger Train = T km/hr
Speed of express Train = T + 11 km/hr
Time taken by Passenger trainn to cover 132 km = 132/T hr
Time taken by Expressr train to cover 132 km = 132/(T + 11) hr
132/T - 132/(T + 11) = 1
=> 132( T + 11 - T) = T(T + 11)
=> 132 * 11 = T² + 11T
=> T² + 11T - 132 * 11 = 0
=> T² + 44T - 33T - 132*11 = 0
=> T(T + 44) - 33(T + 44) = 0
=> (T - 33)(T + 44) = 0
=> T = 33 ( T = -44 not passible as speed can not be - ve)
Speed of Passenger Train = 33 km/hr
Speed of Express train = 33 + 11 = 44 km/hr
Time Taken by Passenger Train = 132/ 33 = 4 hrs
Time taken by Express train = 132/44 = 3 hrs
Total Distance = 132 + 132 = 264 km
Total Time = 4 + 3 = 7 hrs
Average Speed of Both Trains = 264/7
= 37.7 km/Hr
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