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Without stoppages a train travels a certain distance with an average speed of $80 \hspace {0.1cm} km/hr$ and with stoppages with an average speed of $60 \hspace {0.1cm} km/hr$. How many minutes per hour does the train stops?

HOW TO DO CONVENTIONALLY WITHOUT USING DIRECT FORMULA AND SHORTCUT?
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Assume the distance travelled by train is equal to its speed (with stoppages) in an hour which is $60 \hspace {0.1cm} km$. Then , we can find the stoppage time of the train in an hour.

∴ In $80 \hspace {0.1cm} km/hr$ speed (without stoppages) train covers the distance in $\dfrac{60}{80} \hspace {0.1cm} hr = \dfrac{6}{8} \hspace {0.1cm} hr = \dfrac{3}{4} \times 60 \hspace {0.1cm} min = 3 \times 15 \hspace {0.1cm}  min = 45 \hspace {0.1cm} min$ $\qquad \left [  \because Distance = Speed \times Time \\ \qquad \qquad  Or, Time = \dfrac{Distance}{Speed} \right ]$

whereas, in $60 \hspace {0.1cm} km/hr$ speed train covers the distance in $1 \hspace {0.1cm}  hr$.

$\color{maroon}{\text{So, In an hour the train stops for}}$ $\color{green}{ \left ( 60 - 45 \hspace {0.1cm} min \right ) = 15 \hspace {0.1cm}  min}$
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Let total distance = 60 km

time to cover 60 km at speed 80 km/hr (t1)= distance/speed = 60/80 hrs = 3/4 hr

time to cover 60 km at speed 60 km/hr (t2)= distance/speed = 60/60 hrs = 1 hrs

stop time of train per hour = (1 - 3/4 ) hrs

                                         = 1/4 hrs = 15 minutes
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