At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm. Answers: A) 35.21 km/hr. B) 36.21 km/hr. C) 37.21 km/hr. D) 39.21 km/hr. E) 32.21 km/hr.
Let the position of ship B at noon be at the origin   =&gt;ship A has x-coordinate = -100km and B has x-coordinate =0km   At 4.00 p.m., ship A is at x = -100+4*35= 
<gadget id="calculator">-100+4*35</gadget>
<output>40</output>
40km   and B is at x= 0 and y = 4 * 25= 
<gadget id="calculator">4 * 25</gadget>
<output>100</output>
100 km   Distance between them at 4.00 p.m.= √[(100)^2 + (40)^2] = 20√(29) km   Distance between the ships,   s^2 = x^2 + y^2   =&gt; 2s ds/dt = 2x dx/dt + 2y dy/dt   =&gt; rate of change of distance between the ships, ds/dt   = (x dx/dt + y dy/dt) / s   = [40 * 35 + 100 * 25] / [20√(29)] km/hr   = (1400 + 2500) / [20√(29)] km/hr   = 195/√(29) km/hr   ≈ 36.21 km/hr.   ANSWER:36.21 km/hr.
<result>B</result>
At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.