Question

Ankita travels $14$ km to her home partly by rickshaw and partly by bus. She travels $2$ km by rickshaw and the remaining distance by bus. On other hand, she takes $9$ minute longer, if she travels $4$ km by rickshaw and remaining distance by bus. Find the product of the speed of rickshaw and of the bus in $km/hr$

Answer 1

Case-1

Distance travel by ricksaw $d_1=2kmkm$

then distance travel by bus $d_2=14-2=12km$

Case-2

Distance travel by ricksaw $d_1=4km$

then distance travel by bus $d_2=14-4=10km$

Let the speed of ricksaw and bus will be $x$ and $y$ km/hr

And $t_1,t_2$ be the time of his two journey

As per question

$t_2=t_1+9$

Time taken by Ankita in case $1$

$\therefore t_1=\frac{2}{x}+\frac{12}{y}-\left(1\right)$

Time taken by Ankita in case $2$

$\therefore t_2=\frac{4}{x}+\frac{10}{y}\Rightarrow t_1+9=\frac{4}{x}+\frac{10}{y}-\left(2\right)$

(As $t_2=t_1+9$)

Solving eqs.(1) from eqs.(2)

we get $x=\frac{840}{(t_1+54)},y=\frac{840}{(t_1-9)}$

Multiplying $x$ and $y$ we get,

$xy=\frac{(840{)}^2}{(t_1-9)(t_1+54)}$