CBSE Class 8 Answered
an express train takes 1 hour less than a passenger train to travel 132km between Mysore and Banglore(without taking into consideration the time they stop at intermediate stations). if the average speed of the express train is 11km/hr more than that of the passenger train, find the average speeds of the two trains?
Asked by susanta.rkl | 31 Aug, 2018, 10:45: PM
Expert Answer
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
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
Difference between their respective timings is 1 hour
132/x-132/(x + 11)=1
⇒ 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.
⇒ 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.
Answered by Arun | 03 Sep, 2018, 12:00: PM
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