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Question
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 1 1 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.
Solution
Let the arrange speed of express train be denoted by x km/hr
Given that average speed of express train is 11km/hr more than that of the passenger train
⇒ Average speed of passenger train = (x - 11)km/hr
Total distance travelled by the train = 132 km
We know that,
`"Time taken to travel" = "Distance travelled"/"Average speed"=132/x hr`
`rArr"Time taken by express train" ="Distance travelled"/"Average speed of express train"=132/(x-11) hr`
Given that time taken by express train is 1 hour less than that of passenger train.
⇒ Time taken by passenger train - Time taken by express train = 1 hour
`rArr132/(x-11)-132/x=1`
`rArr132(1/(x-11)-1/x)=1`
`rArr132((x-(x-11))/(x(x-11)))=1`
⇒ 132(x - x + 11) = x(x - 11)
⇒ 132(11) = x2 - 11x
⇒ 1452 = x2 - 11x
⇒ x2 - 11x - 1452 = 0
The required quadratic is x2 - 11x - 1452 = 0
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