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 :
Answer & explanation
Correct answer: option 3
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