Helicopter problem

Algebra Level pending

A helicopter travels from point X to point Y at a constant speed of 'A km/hour'. It then travel back from point Y to point X at a constant speed of 'B km/hour'. What is the average speed of the entire journey? (in km/hour)

A + B (A+B) / 2 (A+B) / 3 (2AB) / (A+B)

Connor McCartney by Connor McCartney , 18, Australia

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1 solution

Connor McCartney
Feb 8, 2018

let x = distance from point X to point Y.

Speed (from X to Y) = distance / time 

                         A = x / time

                     time = x / A

Speed (from Y to X) = distance / time 

                           B = x / time

                       time = x / B

Average speed of journey = Total distance / Total time = 2x / ( x A \frac{x}{A} + x B \frac{x}{B} ) = 2x / ( 2 x a b a x + a b \frac{2xab}{ax+ab} ) = x ( 2 a b ) x ( a + b ) \frac{x (2ab)}{x (a+b)} = 2 a b a + b \frac{2ab}{a+b}

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