# Math Help - related rates

1. ## 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?

2. 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:

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

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

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