<aside> ⏳ If two or more time-varying quantities can be related by an equation, then is it possible to find the rate of change of one quantity at a specific moment given information about the other quantities at that moment

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How to approach related rates problems

A ladder is sliding down a wall.

Let the velocity at the top end be denoted by $\frac{dy}{dt}$ and the velocity at the bottom end by $\frac{dx}{dt}$, how are these rates related?

If at some specific moment the bottom end is 0.6 meters from the wall and moving at 3 metres/second outward, how fast is the top end moving?

1. Identify what you are solving for

• Let $x = x(t)$ be the distance along the group from the bottom of the wall to the bottom of the ladder at time $t$
• Let $y(t)$ be the distance along the wall from the floor to the top of the ladder at time $t$
• Assume length of the ladder is 1 metter
  • $x(t_0) = 0.6$
  • $x’(t_0) = 3$