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Distance between two stations A and B is 778km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey.
Answer & Solution
Correct Answer:
Option
D
The required average speed given by the formula,
$$\eqalign{ & {\text{Average speed}} \cr & = {\frac{{2xy}}{{ {x + y} }}} \,\,{\text{km/hr}} \cr & {\text{Where}}, \cr & x = 84{\kern 1pt} \,{\text{kmph}} \cr & y = 56\,{\kern 1pt} {\text{kmph}} \cr & {\text{Average speed}} \cr & = {\frac{{ {2 \times 84 \times 56} }}{{ {84 + 56} }}} \cr & = 67.2\,{\kern 1pt} {\text{kmph}} \cr} $$
$$\eqalign{ & {\text{Average speed}} \cr & = {\frac{{2xy}}{{ {x + y} }}} \,\,{\text{km/hr}} \cr & {\text{Where}}, \cr & x = 84{\kern 1pt} \,{\text{kmph}} \cr & y = 56\,{\kern 1pt} {\text{kmph}} \cr & {\text{Average speed}} \cr & = {\frac{{ {2 \times 84 \times 56} }}{{ {84 + 56} }}} \cr & = 67.2\,{\kern 1pt} {\text{kmph}} \cr} $$
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LoginTotal Time = T1+T2 = 778(1/84+1/56), Total Distance = 2*778
Average speed = Total Distance/Total Time
= 2*778/778(1/84 + 2/56)
= 2/(84+56)/84*56
= 2*84*56/(84+56)
= 67.2