Help needed in Related rates of change problem:

Two quantities p and q are related by the equation (p-1)(q+2) = k where k is a constant. When p = 5 units, q is 7 and q is changing at the rate of 0.04 units per second. Find the rate at which point is changing.

I've tried to work out dp/dt(what the question is asking) as (-36/25) *(q+2)^-2 but that is not what the exercise book is telling me. Can someone please clear this up?

Question

Help needed in Related rates of change problem:

Two quantities p and q are related by the equation (p-1)(q+2) = k where k is a constant. When p = 5 units, q is 7 and q is changing at the rate of 0.04 units per second. Find the rate at which point is changing.

I've tried to work out dp/dt(what the question is asking) as (-36/25) *(q+2)^-2 but that is not what the exercise book is telling me. Can someone please clear this up?

welshfella · Answer

dp/dt  = dq/dt  * dp/dq = 0.04 * dp/dq

welshfella · Answer

Find the value of k:-

(p-1)(q + 2) = k

p = 5 when q = k
so k =  4*9 = 36

welshfella · Answer

p-1)(q + 2) = 36
p- 1 =   36 / (q + 2)

p =  [36 / q + 2]  + 1

Find dp/dq 

and substitute in the formula for dp/dt

anonymous · Answer

That's exactly what I did

welshfella · Answer

I don't understand how you got -36/25     Isnt it -36/81?

welshfella · Answer

(q + 2)^2 = (7 + 2)^2

welshfella · Answer

sorry but i have to go right now.

You have the right method.

anonymous · Answer

dp/dt = dp/dq* dq/dt
= -36(q+2)^-2 * 0.04
=(-36/25)*(q+2)^-2

welshfella · Answer

oh i see
now all you need do is plug in q = 7 and you have your answer