Correct Answer - Option 1 : 52 km/h
Given:
Total distance travelled = 78km
Time = 3 hours 30 minutes = 3 + 30/60 = 7/2 hours
Formula:
Speed = Distance/time
Calculation:
Let speed of Vaibhav and speed of Vignesh be a kmph and (91 - a) kmph respectively.
⇒ 78/a + 78/(91 - a) = 7/2
⇒ 7098 - 78a + 78a = 7/2 × (91a - a2)
⇒ a2 - 91a + 2028 = 0
⇒ a2 - 52a - 39a + 2028 = 0
⇒ a(a - 52) - 39(a - 52) = 0
⇒ (a - 52)(a - 39) = 0
a = 52 or a = 39
Vaibhav's speed is more than Vignesh, so a = 52kmph
∴ Speed of Vaibhav is 52kmph.