**Complicated calculus problem – related rates?**

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*Hey calc freaks, I’m having some trouble with this question…*

The top of a 5 m wheeled ladder rests against a vertical wall. If the bottom of the ladder rolls away at 1/3 m/s, how fast is the top of the ladder sliding down the wall when it is 3m above the base of the wall?

Thanks!

a=4

da/dt=1/3

b=3

db/dt=?

c=5

dc/dt=0, c is constant

using pythagorean theorem

a=4

a²+b²=c², take the derivative with respect to time

2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

2(4)(1/3)+2(3)(db/dt)=2(5)(0)

8/3 + 6(db/dt)=0

db/dt= 4/9 m/s

**How to solve related rate calculus word problems**

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