Ankita travels 14 ,km to her home partly by r | vedclass

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

Question

(B) Let the speed of the rickshaw be $x \,km/h$ and the speed of the bus be $y \,km/h$.Time taken to travel $2 \,km$ by rickshaw is $t_1 = \frac{2}{x}

Vedclass · Accepted Answer

$10, 40$

Vedclass · Answer

(B) Let the speed of the rickshaw be $x \,km/h$ and the speed of the bus be $y \,km/h$.Time taken to travel $2 \,km$ by rickshaw is $t_1 = \frac{2}{x} \,h$.Time taken to travel the remaining distance $(14 - 2) = 12 \,km$ by bus is $t_2 = \frac{12}{y} \,h$.According to the first condition: $\frac{2}{x} + \frac{12}{y} = \frac{1}{2} \quad ...(i)$Time taken to travel $4 \,km$ by rickshaw is $t_3 = \frac{4}{x} \,h$.Time taken to travel the remaining distance $(14 - 4) = 10 \,km$ by bus is $t_4 = \frac{10}{y} \,h$.Since she takes $9 \,minutes$ longer,the total time is $\frac{1}{2} + \frac{9}{60} = \frac{1}{2} + \frac{3}{20} = \frac{13}{20} \,h$.According to the second condition: $\frac{4}{x} + \frac{10}{y} = \frac{13}{20} \quad ...(ii)$Let $u = \frac{1}{x}$ and $v = \frac{1}{y}$. The equations become:$2u + 12v = \frac{1}{2} \quad ...(iii)$$4u + 10v = \frac{13}{20} \quad ...(iv)$Multiply equation $(iii)$ by $2$: $4u + 24v = 1 \quad ...(v)$Subtract $(iv)$ from $(v)$:$(4u + 24v) - (4u + 10v) = 1 - \frac{13}{20}$$14v = \frac{7}{20} \Rightarrow v = \frac{7}{20 	imes 14} = \frac{1}{40}$.Thus,$y = 40 \,km/h$.Substitute $v = \frac{1}{40}$ into $(iii)$:$2u + 12(\frac{1}{40}) = \frac{1}{2} \Rightarrow 2u + \frac{3}{10} = \frac{1}{2}$$2u = \frac{1}{2} - \frac{3}{10} = \frac{5-3}{10} = \frac{2}{10} = \frac{1}{5}$$u = \frac{1}{10}$. Thus,$x = 10 \,km/h$.The speed of the rickshaw is $10 \,km/h$ and the speed of the bus is $40 \,km/h$.

Similar Questions

Graphically,solve the following pair of equations:
$2x + y = 6$
$2x - y + 2 = 0$
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the $x$-axis and the lines with the $y$-axis.

Solve the following pair of linear equations by the elimination method and the substitution method:
$3x + 4y = 10$ and $2x - 2y = 2$

Write a pair of linear equations which has the unique solution $x = -1, y = 3$. How many such pairs can you write?

Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.

The pair of equations $ax - y = 5$ and $4x - 2y = 10$ has an infinite number of solutions. Then $a = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module