Last updated at Feb. 25, 2017 by Teachoo

Transcript

Ex 4.3 ,10 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 train is 11km/h more than that of the passenger train, find the average speed of the two trains. Let the average speed of passenger train = x km/h Given that , express train taken 1 hour less โด Time taken by passenger train โ Time taken by express = 1 train 132/๐ฅ โ 132/(๐ฅ + 11)=1 (132(๐ฅ + 11) โ 132๐ฅ)/(๐ฅ(๐ฅ + 11))=1 (132๐ฅ + 132(11) โ 132๐ฅ)/(๐ฅ(๐ฅ + 11))=1 (132๐ฅ โ 132๐ฅ + 1452)/(๐ฅ(๐ฅ + 11))=1 1452/(๐ฅ(๐ฅ + 11))=1 1452 = x(x + 11) 1452 = x2 + 11x 0 = x2 + 11x โ 1452 x2 + 11x โ 1452 = 0 We solve this by quadratic method Comparing equation with ax2 + bx + c = 0, Here a = 1, b = 11, c = โ1452 We know that D = b2 โ 4ac D = (11)2 โ 4 ร 1 ร (โ1452) D = 121 + 5808 D = 5929 So, the roots to equation are x = (โ๐ ยฑ โ๐ท)/2๐ Putting values x = (โ11 ยฑ โ5929)/(2 ร 1) x = (โ11 ยฑ โ5929)/2 x = (โ11 ยฑ 77)/2 Solving So, x = 33 & x = โ 44 So, x = 33 & x = โ 44 is the roots of the equation Since x is the average speed of the passenger train, it cannot be negative So, x = 33 Average speed of passenger train = x = 33 km/hr So, average speed of express train = x + 11 = 33 + 11 = 44 km/hr

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.