# 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

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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:
1. 52 km/h
2. 48 km/h
3. 54 km/h
4. 45 km/h

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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.