Question 103550
A cyclist rides D km at a rate of X km/hr and returns D km at a rate of Y km/hr. Write an expression representing the average rate in terms of X,Y and D. Simplify this expression if you can. 
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1st ride DATA;
Rate = X km/h ; Distance = D miles ; Time = D/R = D/X hrs
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Return ride DATA:
Rate = Y km/h ; Distance = D miles ; Time = D/R = D/Y hrs
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Average Rate = (total distance) / (total time) = 2D/[D/X + D/Y]
= 2D/[D(Y+X)/XY]

= 2XY/(X+Y)

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Cheers,
Stan H.