Question

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

Answer 1

Let the speed of the rickshaw be $x$ km/min and the speed of the bus be $y$ km/min.

As given in the problem,
since time $=\frac{distance}{speed}$,

$\frac{2}{x}+\frac{12}{y}=30$

$\frac{4}{x}+\frac{10}{y}=39$

Substituting $\frac{1}{x}$ as u and $\frac{1}{y}$ as v (Where $x\ne 0,y\ne 0)$, we get
$2u+12v=30$ …(1)
$4u+10v=39$ …(2)

Multiplying equation (1) by 2,
we get
$4u+24v=60$ …(3)

Subtracting equation (2) from equation (3),
we get
$14v=21$
$\Rightarrow v=\frac{3}{2}$

Putting $v=\frac{3}{2}$ in the equation (1),
we get

$2u+12\times \frac{3}{2}=30$
$\Rightarrow 2u=30-18$
$\Rightarrow u=\frac{12}{2}=6$.

Therefore,
$x=\frac{1}{6}$ km/min and $y=\frac{2}{3}$ km/min.

To get the speed in km/hr, we multiply each speed with 60 since 1 hr = 60 min.

Therefore,
$x=\frac{1}{6}\times 60=10$ km/hr

$y=\frac{2}{3}\times 60=40$ km/hr