# Flying

The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?

Result

v =  840 km/h

#### Solution:

$s/(v-60) + s/(v+70) = 2s/v \ \\ 1/(v-60) + 1/(v+70) = 2/v \ \\ v(v+70)+v(v-60) = 2 \cdot \ (v+70)(v-60) \ \\ 10v = 8400 \ \\ v = 8400 / 10 = 840 \ \\ = 840 \ \text{ km/h }$

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