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# An airplane travels at an average speed of 600 m/s on an outward flight and 400 m/s on the return flight over the same distance. What's is the average speed of the whole flight?

## Note that the answer is not 500m/s but 480 m/s. Please explain why not?

Dec 4, 2017

let the distance travelled by the the plane during
outward flight$\rightarrow$s

Also distance travelled during return flight$\rightarrow$s

average speed$=$$\frac{\text{Total distance}}{T o t a l t i m e}$

Average speed{v}$\Rightarrow$$\frac{s + s}{\left(\frac{s}{v} _ 1\right) + \left(\frac{s}{v} _ 2\right)}$
V=(2s)/(s((v_1+v_2)/(v_1v_2))

color(red)(V=(2v_1v_2)/(v_1+v_2)

substituting values of v_1 & v_2:

$\Rightarrow \frac{2 \times 600 \times 400}{600 + 400}$ =color(green)(480(m)/(s)