Doubts

[ravihanda]

Please go through the solved examples before asking a doubt.

[manish rane]

A horse rider travels from pune to banglore at constant speed. if the horse increase the speed by 6km/hr it would take rider 4 hrs less and if the it travels with speed less by 6km/hr it would take rider 10hr more to reach banglore.Find the distance between two cities.


manish

[ravihanda]

A horse rider travels from pune to banglore at constant speed. if the horse increase the speed by 6km/hr it would take rider 4 hrs less and if the it travels with speed less by 6km/hr it would take rider 10hr more to reach banglore.Find the distance between two cities.

Let us say that the distance is d between the two cities and the speed is s.

d/(s+6) = d/s - 4
d/(s-6) = d/s + 10

I have two equations and two variables, I can solve it.
A smarter way to solve it would be using the idea of Harmonic Mean. If I look at the three speeds they are s-6,s and s+6 which are in AM. The times taken are t+10, t and t-4. If speeds are in AM, distance is constant, Time taken would be in Harmonic mean.
So, t = 2(t-4)(t+10) / [t-4+t+10]
=> t x (2t + 6) = 2 (t^2 +6t - 40)
=> t^2 + 3t = t^2 + 6t - 40
=> 3t = 40 => t = 40/3 hrs.
So, the times taken are 70/3, 40/3 and 28/3
So, s+6/s-6 = 70/28 = 5/2
2s + 12 = 5s - 30
3s = 42
s = 14 km /hr.

Distance 14 x 40 / 3 = 560/3 km