Question

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half a 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.
Since Time = $\frac{Distance}{Speed}$
$\frac{2}{x}+\frac{12}{y}=30$
$\frac{4}{x}+\frac{10}{y}=39$

(where x $\ne 0,y\ne 0$)
Substituting $\frac{1}{x}asuand\frac{1}{y}asv,$ we get
2u + 12v = 30 .... (1)
4u + 10v = 39 .... (2)
Multiplying equation (1) by 2, we get 4u + 24v = 60 ... (3)
Substracting equation (2) from equation (3), we get
14v = 21 $\Rightarrow v=\frac{3}{2}$
Putting $v=\frac{3}{2}$ in equation (1), we get $2u+12\times \frac{3}{2}=30$
$\Rightarrow$ 2u = 30 - 18
$\Rightarrow$ $u=\frac{12}{6}=6$

$\therefore$ $x=\frac{1}{6}$km/min and $y\frac{2}{3}$ km/min
To get the speed in km/hr, we multiply each speed by 60, since 1 hr = 60 min.
$x=\frac{1}{6}\times 60=10$ km/hr
$y=\frac{2}{3}\times 60=40$ km/hr