Riyana travels 100 km by bike and rest by car out of 400 km distance in 6.5 hours. If she travels 150 km by bike and rest by car, she takes 15 minutes more . The speed of the bike is :

50 km/hr

Distance = Speed × Time 

Let speed of byke = b km/hr and speed of car = c km/hr

According to question ,

\(\frac{100}{b}\)  +  \(\frac{300}{c}\)  =  6 . 5 hours   = \(\frac{13}{2}\)

Put \(\frac{1}{b}\) = B and \(\frac{1}{c}\) = C

200B  +  600C  =  13      -------- ( 1 ) 

If she travels 150 km by byke and rest by car, she will take 15 minutes more . 

i.e. time taken is 6 hours 45 min  = \(\frac{27}{4}\) hours 

\(\frac{150}{b}\)  +  \(\frac{250}{c}\)  =  \(\frac{27}{4}\) hours   

600B + 1000C =  27        ------ ( 2 ) 

Multiply equation 1 by 5 and and equation 2 by 3  then subtract it from equation 1 . we get , 

1800B - 1000B = 81 - 65 

800B = 16 

b =  \(\frac{800}{16}\)  = 50 km/hr

hence speed of byke = 50 km/hr