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An urgent message had to be delivered from the house Of the Peshwas in Pune to Shivaji who was camping in Bangalore. A horse rider travels on horse back from Pune to Bangalore at a constant speed. If the horse increased its speed by $6km/h$, it would take the rider $4$ hours less to cover that distance. And travelling with a speed $6 km/h$ lower than the initial speed, it would take him $10 hours$ more than the time he would have taken had he travelled at a speed $6kmph$ higher than the initial speed. Find the distance between Pune and Bangalore.

I tried my best to solve this in a very short period of time but I couldn't do it all. Such a long process. Then I understood that it could be done using the concept of integral difference in ratios Where I end up with wrong result.

I might be wrong with the equations I am forming: $$(d/s)-(d/(s+6))=4$$ $$(d/(s-6))-(d/(s+6))=10$$

$$6d=5(s^2-36) \quad ----2$$ $$6d=4s(s+6) \quad ----1$$

from one and two equations, s= 6 and -30

what next?

Joypal
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I agree with your 2 equations. The first one simplifies to $6d=4s(s+6)$. The second one can be replaced by $(d/(s-6))-(d/s)=6$ (its difference with the first one), which simplifies to $6d=6s(s-6)$. The system is now easy to solve: $s=30,d=720$.

Anne Bauval
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I think the velocity times time equals distance formula is easier.

$v t=d$

$(v+6)(t-4) =d$

$(v-6) (t-4+10)=d$

Solve those three equations for $v$,$t$,and $d$(velocity, time, distance), you will get 30, 24, and 720 respectively.

Bill Watts
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  • I didnt understand, could you be little more in detail. – Joypal Sep 06 '22 at 04:58
  • What exactly don't you understand? Do you know the formula velocity * time = distance? All three equations represent that. The first represents the original velocity and time. The second increases the velocity by 6 and reduces the time by 4. The third reduces the original velocity by 6 and increases the time of the second case by 10. Of course, the distance is the same in all three cases. – Bill Watts Sep 06 '22 at 07:26