Two trains each make a journey of 330km. One of the trains travels 5km/h faster than the other and takes 30 minutes less. Find the speed of the trains.

Answer:S 1 =  [tex]\frac{330}{6}[/tex] =55 km/hS 2 = 55 km/h + 5 km/h = 60 km/h   Step-by-step explanation:Given as,Distance cover by both Trains = D1 = D2 =330 kmSpeed of Train 1 = S  km/h                        Speed of Train 2 = (S + 5) km/hTime taken by Train 1 = T hour    Time take by Tain 2 =T - [tex]\frac{1}{2}[/tex] hNow Distance = Speed × TimeSo, S ×T =  (S + 5) ( T - [tex]\frac{1}{2}[/tex] )Or, [tex]\frac{S}{2}[/tex] + [tex]\frac{5}{2}[/tex] = 5 Ti.e S + 5 = 10 TAs, D = S× TSo, 330 = ( 10T - 5 ) × T = 10T² - 5TOr 2 T² - T = 66      2 T² - 12 T +11 T - 66 = 0 Or,  2T (T - 6 ) + 11 ( T - 6 ) = 0Or,   T = 6 , -  5.5 hourSO S 1 =  [tex]\frac{330}{6}[/tex] =55 km/h      S 2 = 55 km/h + 5 km/h = 60 km/h    Answer