A train travels at a certain average speed fo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the original average speed of the train be $x \, km/h$.According to the problem,the time taken for the first part is $\frac{63}{x} \, hours$ a

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(B) Let the original average speed of the train be $x \, km/h$.According to the problem,the time taken for the first part is $\frac{63}{x} \, hours$ and for the second part is $\frac{72}{x+6} \, hours$.The total time taken is $3 \, hours$,so:$\frac{63}{x} + \frac{72}{x+6} = 3$Dividing the entire equation by $9$:$\frac{7}{x} + \frac{8}{x+6} = \frac{1}{3}$Multiplying by $3x(x+6)$ to clear the denominators:$21(x+6) + 24x = x(x+6)$$21x + 126 + 24x = x^2 + 6x$$45x + 126 = x^2 + 6x$$x^2 - 39x - 126 = 0$Factoring the quadratic equation:$(x - 42)(x + 3) = 0$This gives $x = 42$ or $x = -3$.Since speed cannot be negative,the original average speed is $42 \, km/h$.

$A$ train travels at a certain average speed for a distance of $63 \, km$ and then travels a distance of $72 \, km$ at an average speed of $6 \, km/h$ more than its original speed. If it takes $3 \, hours$ to complete the total journey,what is its original average speed in $km/h$?

Similar Questions

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

Solve the following equation using the method of factorization: $x^{2} + (x + 5)^{2} = 125$

State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

If the discriminant of $x^{2}-10x+(2k-1)=0$ is $40$,then $k=$...............

Vedclass Test Series

Exam Paper Generator

Online Exam Module