Question

A train travels 112 km in 1 hour 30 minutes with a certain speed. How many kilometres it will travel in 4 hours 45 minutes with the same speed?

Answer 1

Solution: Let the required distance be x km.

$\text{More distance}\to \text{more time}$

Thus, the two quantities are directly proportional.

Distance (in km)	112	x
Time (in hours)	$\frac{3}{2}h$	$\frac{19}{4}h$

$\left[\begin{array}{c}\because 1\text{hr}30\text{min}=\frac{3}{2}h\\ 4\text{hr}45\text{min}=\frac{19}{4}h\end{array}\right]$

$\frac{x_1}{y_1}=\frac{x_2}{y_2}$

$\Rightarrow \frac{112}{x}=\frac{1.5}{\frac{19}{4}}$

$\Rightarrow \frac{3}{2}x=112\times \frac{19}{4}$

$=354.6km.$

Hence, the required distance =354.6 km.