Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, hour before the second rabbit reaches A. If the distance between A and B is 50 km. what is the speed of the slower rabbit?

Created: 3 months ago | Updated: 3 months ago

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প্রশ্নে বলা হচ্ছে যে, দুটি খরগোশের একটি A হতে B তে এবং অপরটি B হতে B তে যাচ্ছে। একঘণ্টা পর তারা পরষ্পর একে অপরকে অতিক্রম করলো। প্রথম খরগোশটি দ্বিতীয় খরগোশের চেয়ে ঘণ্টা বা 50 মিনিট পূর্বেই B স্থানে পৌছাল । A এবং B এই স্থান দুটির মধ্যবর্তী দূরত্ব 50 km হলে ধীরগতির খরগোশটির গতিবেগ কত ?
প্রথমেই প্রশ্ন অনুযায়ী নিচের মতো করে চিত্র আঁকুনঃ

Let, another rabbit takes x hours to go it's destination.

∴ One rabbit takes $(x - \frac{5}{6})$ hours to go it's destination.

As one rabbit reaches $\frac{5}{6}$ hours or 50 minutes before another rabbit, so one rabbit is faster and another one is slower.

Now, we assume that the speed of one rabbit is v₁ kmph and the speed of another rabbit is v₂ kmph.

$A s v e l o c i t y = \frac{d i s \tan c e}{t i m e} ∴ v_{1} = \frac{50}{x - \frac{5}{6}} k m p h . . . . . . . . . . . (i) A n d v_{2} = \frac{50}{x} k m p h . . . . . . . . . . . . (i i) A s t h e y a r e c o m i n g t o w a r d s o n e a n o t h e r, t h e i r r e l a t i v e s p e e d w i l l b e (v_{1} + v_{2}) k m p h . N o w, a c c o r d i n g t o q u e s t i o n \Rightarrow \frac{50}{v_{1} + v_{2}} = 1 \Rightarrow \frac{50}{(\frac{50}{x - \frac{5}{6}}) + (\frac{50}{x})} = 1 \Rightarrow \frac{50}{50 (\frac{1}{x - \frac{5}{6}} + \frac{1}{x})} = 1 \Rightarrow \frac{1}{x - \frac{5}{6}} + \frac{1}{x} = 1 \Rightarrow \frac{1}{\frac{6 x - 5}{6}} + \frac{1}{x} = 1 \Rightarrow \frac{6}{6 x - 5} + \frac{1}{x} = 1 \Rightarrow \frac{6 x + 6 x - 5}{(6 x - 5) x} = 1 \Rightarrow \frac{12 x - 5}{6 x^{2} - 5 x} = 1 \Rightarrow 6 x^{2} - 5 x - 12 x + 5 = 0 \Rightarrow 6 x^{2} - 17 x + 5 = 0 \Rightarrow 6 x^{2} - 15 x - 2 x + 5 = 0 \Rightarrow 3 x (2 x - 5) - 1 (2 x - 5) = 0 ∴ (2 x - 5) (3 x - 1) = 0 S o, t h e v a l u e o f x w i l l b e e i t h e r \frac{5}{2} o r \frac{1}{3} . [B u t x = \frac{1}{3} i s n o t a c c e p t a b l e] N o w, w e w i l l p u t v a l u e x = \frac{5}{2} i n e q u a t i o n (i i) t o g e t t h e s p e e d o f t h e s l o w e r r a b b i t . ∴ v_{2} = \frac{50}{\frac{5}{2}} = \frac{50}{1} \times \frac{2}{5} = 20 k m p h ∴ T h e s p e e d o f t h e s l o w e r r a b b i t i s 20 k m p h .$

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Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, hour before the second rabbit reaches A. If the distance between A and B is 50 km. what is the speed of the slower rabbit?

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