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AP Calculus AB· difficulty 3/5

Boat A heads east at 15 km/h15~\text{km/h}, boat B heads north at 20 km/h20~\text{km/h}, both starting at the same point. After 2 hours, the rate of separation is

  • A

    35 km/h35~\text{km/h}

  • B

    25 km/h25~\text{km/h}

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  • C

    10 km/h10~\text{km/h}

  • D

    50 km/h50~\text{km/h}

Explanation

D=(xx+yy)/DD' = (x x' + y y')/D. After 2 h: x=30,y=40,D=50x = 30, y = 40, D = 50. D=(30(15)+40(20))/50=(450+800)/50=25D' = (30(15) + 40(20))/50 = (450 + 800)/50 = 25.

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