Question

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km per hour more than its original speed if it takes 3 hour to complete total jana what is the general average speed

Answer 1

${\bold{\huge{\underline{\green{Answer!!}}}}}$

$\large\bf\implies\:t_1\:=\frac{63}{x}$

$\large\bf\implies\:t_2\:=\frac{72}{x+6}$

$<b><u>Now add,$

$\large\sf\implies\:t_1\:+t_2\:=\frac{63}{x}+\frac{72}{x+6}$

$\large\sf\implies\:3\:=\frac{63(x+6)+72x}{x(x+6)}$

$\large\sf\implies\:3x^{2}\:+\:18x\:=\:63x\:+378\:+72x$

$\large\sf\implies\:3x^{2}\:+\:18x\:-135x\:-378\:=0$

$\large\sf\implies\:3x^{2}\:-117x\:-378\:=\:0$

$\large\sf\implies\:3x\:+\:9x\:-126x\:-378\:=\:0$

$\large\sf\implies\:3x\:(x\:+3)\:-126\:(x\:+3)=0$

$\large\sf\implies\:(x+3)\:(3x-126)\:=\:0$

$\large\sf\implies\:3x\:=\:126$

$\large\bf\implies\:x\:=\frac{126}{3}$

$\large\bf\implies\:x\:=\:42\: km/hr$

Answer 2

Let the original speed of train is x km/h
time taken to cover 63 km with speed x km/h, T₁ = distance/time = 63/x hours

Again, question said , speed of train now (x + 6) km/h
Time taken to cover 72km with speed (x + 6) km/h , T₂= 72/(x + 6) km/h

A/C to question ,

T₁ + T₂ = 3 hours

⇒63/x + 72/(x + 6) = 3
⇒ 21/x + 24/(x + 6) = 1
⇒ (21x + 126 + 24x) = x(x + 6)
⇒45x + 126 = x² + 6x
⇒ x² - 39x - 126 = 0
⇒x² - 42x + 3x - 126 = 0
⇒ x(x - 42) + 3(x - 42) = 0
⇒(x + 3)(x - 42) = 0

∴x = 42 and -3 , but x ≠ -3 ∵ speed doesn't negative

Hence, original speed of train = 42 km/h