an Express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km per hour more than that of the passenger train, form the quadratic equation to find the average speed of Express train
Answers
Let the Average Speed of the passenger train be x
Average Speed of express train = x+11
Total distance traveled = 132 kms
Time taken by passenger train = Distance/Speed = 132/x
Time Taken by express train = Distance/Speed = 132/(x+11)
As the passenger train takes 1 hr more to cover the same distance:
132/x = 132/(x+11) + 1
132/x = (132+x+11)/(x+11)
132(x+11) = x(x+143)
132x + 1452 = x^{2} + 143x
1452 = x^{2} + 11x
x^{2} +11x-1452=0
x^{2} +44x-33x-(44*33)=0
(x+44)(x-33)=0
So x can be either -44 or 33. As x represents the average speed of passenger train, it cannot be negative.
Hence the speed of the passenger train is 33km/hr
And the speed of the express train is 33+11 = 44km/hr
Answer:
Step-by-step explanation:
Let the speed of passenger train be x km/hr Hence speed of express train = (x +11) km/hr Distance travelled by both the trains = 132 km Time taken = (Distance)/(Speed) Time taken by the passenger train = 132/x hrs Time taken by the express train = 132/(x + 11) hrs ⇒ 132 × 11 = x(x + 11) ⇒ x2 + 11x – 1452 = 0 ⇒ x2 + 44x – 33x – 1452 = 0 ⇒ x(x + 44) – 33(x + 44) = 0 ⇒ (x + 44)(x – 33) = 0 ⇒ (x + 44) = 0 or (x – 33) = 0 ∴ x = –44 or x = 33 Since speed cannot be negative, x = 33 Thus the sped of passenger train is 33 km/hr and speed of express train is 44 km/hr.