Solve the following Mathematical Problems

After traveling 108 km, a cyclist observed that he would have required 3 hours less if he could have traveled at a speed 3 km/hr more. At what speed did he travel?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নে বলা হচ্ছে যে, 108 কিলোমিটার যাওয়ার পরে একজন সাইকেল আরোহী বুঝতে পারলেন যে তিনি যদি 3 km/hr বেশি বেগে যেতেন, তবে তার 3 ঘণ্টা কম সময় লাগতো। সাইকেল আরোহীর গতিবেগ কত ?

$L e t, t h e s p e e d b e x k m / h r . S i n c e d i s \tan c e i s 108 k m, t i m e = \frac{108}{x} h r s W h e n s p e e d i s i n c r e a s e d b y 3 k m / h r, s p e e d i s = (x + 3) k m / h r ∴ T h e r e q u i r e d t i m e = \frac{108}{x + 3} h r s A c c o r d i n g t o t h e q u e s t i o n, \frac{108}{x} - \frac{108}{x + 3} = 3 \Rightarrow \frac{108 (x + 3) - 108 x}{x (x + 3)} = 3 \Rightarrow \frac{108 x + 324 - 108 x}{x^{2} + 3 x} \Rightarrow 324 = 3 x^{2} - 9 x \Rightarrow 324 - 3 x^{2} - 9 x = 0 \Rightarrow - 3 x^{2} - 9 x + 324 = 0 \Rightarrow - 3 (x^{2} + 3 x - 108) = 0 \Rightarrow x^{2} + 3 x - 108 = 0 \Rightarrow x^{2} + 12 x - 9 x - 108 = 0 \Rightarrow x (x + 12) - 9 (x + 12) \Rightarrow (x + 12) (x - 9) = 0 S o e i t h e r, x - 9 = 0 o r, x + 12 = 0 i f, x + 12 = 0 t h e n, x = - 12 ∴ T h e s p e e d 9 k m [S i n c e v e l o c i t y x \neq - 12] H e t r a v e l e d a t a s p e e d o f 9 k m / h r . (a n s)$