Vaibhav and Vignesh each travel a distance of 78 km such that the speed of Vaibhav is faster than that of Vignesh. The sum of their speeds is 91 km/h and the total time taken by both is 3 hours and 30 minutes. The speed of Vaibhav is:

52 km/h

Total time taken = 3 hours 30 minutes = \(\frac{7}{2}\) hours

Let speed of vaibhav = S km/h . So , Speed of Vignesh = ( 91 - S ) km/h

According to question ,

\(\frac{78}{S}\) +  \(\frac{78}{91 - S }\) = \(\frac{7}{2}\)

\(\frac{78 × 91 }{S (91 - S ) }\) = \(\frac{7}{2}\)

\(\frac{78 × 13 }{S (91 - S )}\) = \(\frac{1}{2}\)

78 × 26 = S ( 91 - S )

On solving , possible values of S are 

S = 52 & 39

But we know , Speed of vaibhav is more than speed of vignesh .

So , Speed of vaibhav is 52 km/h