Question

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 1

S 1 =
`(330)/(6)` =55 km/h

S 2 = 55 km/h + 5 km/h = 60 km/h

Explanation:

Given as,

Distance cover by both Trains = D1 = D2 =330 km

Speed of Train 1 = S km/h Speed of Train 2 = (S + 5) km/h

Time taken by Train 1 = T hour Time take by Tain 2 =T -
`(1)/(2)` h

Now Distance = Speed × Time

So, S ×T = (S + 5) ( T -
`(1)/(2)` )

Or,
`(S)/(2)` +
`(5)/(2)` = 5 T

i.e S + 5 = 10 T

As, D = S× T

So, 330 = ( 10T - 5 ) × T = 10T² - 5T

Or 2 T² - T = 66

2 T² - 12 T +11 T - 66 = 0

Or, 2T (T - 6 ) + 11 ( T - 6 ) = 0

Or, T = 6 , - 5.5 hour

SO S 1 =
`(330)/(6)` =55 km/h

S 2 = 55 km/h + 5 km/h = 60 km/h Answer