An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is 42 cm and each wheel makes 1200 revolutions per minute, find the speed of the train.

Diameter of wheel = 42 cm

Radius of wheel = $\dfrac{d}{2}$ = $\dfrac{42}{2}$ = 21 cm

Circumference of wheel = 2πr

$= 2 \times \dfrac{22}{7} \times 21\\[1em] = 2 \times 22 \times 3\\[1em] = 132 \text{ cm}$

Total distance covered by one wheel in 1 minute = Number of revolutions x Circumference of wheel

= 1,200 x 132 cm

= 158,400 cm

= 1.584 km

Speed of the train = $\dfrac{\text{Distance}}{\text{Time}}$

= $\dfrac{1.584}{\dfrac{1}{60}}$

= $\dfrac{1.584 \times 60}{1}$

= 95.04 km/hr

Hence, the speed of the train is 95.04 km/hr.