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Related Rates Boat Question Help!? | Yahoo Answers
Draw the diagram.
You have a right triangle where the hypotenuse is the distance between the ships.
Label the hypotenuse x. You want to find dx/dt.
let B = the distance ship B has travels. dB/dt = 15
let A = the distance ship A travels. dA/dt = 19
At 6 pm, both ships have traveled for 6 hours which means B=6(15)=90 and A=30+6(19)=126.
use the Pythagorean theorem:
A² + B² = x²
At 6 hours, x² = 126² + 90², x = 154.8
2A(dA/dt) + 2B(dB/dt) = 2x(dx/dt)
plug in known values:
2(126)(19) + 2(90)(15) = 2(154.8)(dx/dt)
solve for dx/dt:
dx/dt = 24.186