Rishika travels 250 km by train and rest by car out of 550 km distance in 6 hours. If she travels 310 km by train and rest by car, she takes 12 minutes less. The speed of the train is :

110 km/hr

Distance = Speed × Time 

Let speed of train = t km/hr and speed of car = c km/hr

According to question ,

\(\frac{250}{t}\)  +  \(\frac{300}{c}\)  =  6 hours   

Put \(\frac{1}{t}\) = T and \(\frac{1}{c}\) = C

250T  +  300C  =  6   -------- ( 1 ) 

If she travels 310 km by train and rest by car, she will take 12 minutes less . 

i.e. time taken is 5 hours 48 min  = \(\frac{29}{5}\) hours 

\(\frac{310}{t}\)  +  \(\frac{240}{c}\)  =  \(\frac{29}{5}\) hours   

310T + 240C =  \(\frac{29}{5}\) 

1550T  +  1200C = 29    ------ ( 2 ) 

Multiply equation 1 by 3 and then subtract it from equation 2 . we get , 

550T  = 5 

T =  \(\frac{5}{550}\) 

t =  \(\frac{550}{5}\)  = 110 km/hr 

hence , speed of train = 110 km/hr