[Math] Related Rates – Ships

calculusderivatives

Ship A is currently 85 km south of ship B. Ship A travels north at 30 km/h and ship B travels east at 20 km/h. How fast is the distance between them changing in 1.5 hours?

I have established the givens but I'm not completely sure how to proceed with this related rates problem. Do I use Pythagoras or what exactly should I do…if I understand the process I can do more practice

Thanks

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Best Answer

HINT:

You start with Pythagorean Theorem,

$$a^2 + b^2 = c^2$$

Then you take the derivative of both sides, and divide both sides by 2,

$$2a\frac{da}{dt} + 2b\frac{db}{dt} = 2c\frac{dc}{dt}$$ $$a\frac{da}{dt} + b\frac{db}{dt} = c\frac{dc}{dt}$$

Now you solve for the rate at which the distance between them is changing,

$$\frac{a\frac{da}{dt} + b\frac{db}{dt}}{c} = \frac{dc}{dt}$$

Then, you substitute your values into this equation. Hope this helps!

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