An aeroplane flies from A to B at the rate of 500 km/ hour and comes back from B to A at the rate of 700 km/ hour. The average speed of the aeroplane is......?

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Answer 1 · 2018-06-08T03:54:22

From A to B in $x$ $x$ hours covers distance $500 x$ $500x$ km

From B to A in $y$ $y$ hours covers distance $700 y$ $700y$ km

But since the distance back and forwards is the same

$500 x = 700 y$ $500x=700y$

$y = \frac{5}{7} x$ $y=5/7x$

Average distance =(total distance)/(total time)

Average distance = $\frac{500 x + 700 y}{x + y}$ $(500x+700y)/(x+y)$

But $y = \frac{5}{7} x$ $y=5/7x$

Hence

Average distance= $\frac{7000}{12}$ $7000/12$ km/hr