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  1. #1
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    related rates

    At noon, ship A is 150 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 25 km/h. After two hours, they are approximately 121 km apart. How fast is the distance between the ships changing after two hours?
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  2. #2
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    We can use Pythagoras:

    D^{2}=x^{2}+y^{2}

    After two hours, A has traveled 40 km and B has traveled 50 km.

    Therefore, At two hours the distance between them is:

    \sqrt{(150-40)^{2}+50^{2}}=10\sqrt{146}\approx{120.83} \;\ km

    differentiate:

    D\frac{dD}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}

    10\sqrt{146}\frac{dD}{dt}=110(20)+50(25)

    \frac{dD}{dt}=\frac{345}{\sqrt{146}}\approx{28.55} \;\ km/hr
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