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.
[3 Marks]

Answer 1

Let the speed of the rickshaw be x km/min and the speed of the bus be y km/min.
Since time = 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, we get (Where $x\ne 0,y\ne 0)$
$2u+12v=30\dots \left(1\right)$
$4u+10v=39\dots \left(2\right)$ [0.5 Marks]

Multiplying equation (1) by 2, we get $4u+24v=60\dots \left(3\right)$
Subtracting equation (2) from equation (3), we get 14v = 21 $\Rightarrow v=\frac{3}{2}$ [0.5 Marks]

Putting $v=\frac{3}{2}$ in equation (1), we get,
$2u+12\times \frac{3}{2}=30\Rightarrow 2u=30-18$
$\Rightarrow u=\frac{12}{2}=6$. [0.5 Marks]

Therefore, $x=\frac{1}{6}km/minandy=\frac{2}{3}km/min$. [1 Mark]

To get the speed in km/hr, we multiply each speed with 60, since 1 hr = 60 min.
Therefore,
$x=\frac{1}{6}\times 60=10km/hr$
$y=\frac{2}{3}\times 60=40km/hr$ [0.5 Marks]