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

Answer:

S 1 =  $\frac{330}{6}$ =55 km/h

S 2 = 55 km/h + 5 km/h = 60 km/h  

Step-by-step 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 - $\frac{1}{2}$ h

Now Distance = Speed × Time

So, S ×T =  (S + 5) ( T - $\frac{1}{2}$ )

Or, $\frac{S}{2}$ + $\frac{5}{2}$ = 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 =  $\frac{330}{6}$ =55 km/h

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