Word problem using derivatives - struggling with it

[meredith]

Homework Statement

the equation is PV = c; p = pressure, v = volume, c=constant. (also known as Boyle's law)
the question: if volume is decreasing at a rate of 10cm^3/minute, how fast is the pressure increasing when the pressure is 100g/cm^2 and volume is 20 cm^3

Homework Equations

none

The Attempt at a Solution

dv/dt = -10cm^3/min
dp/dt = ?
equation: PV=c
derivative:
dp/dt x dv/dt = 0
dp/dt = -dv/dt

but i know what I am doing isn't right. can anyone help me? THANKS!

 

[Mark44]

Homework Statement

the equation is PV = c; p = pressure, v = volume, c=constant. (also known as Boyle's law)
the question: if volume is decreasing at a rate of 10cm^3/minute, how fast is the pressure increasing when the pressure is 100g/cm^2 and volume is 20 cm^3

Homework Equations

none

The Attempt at a Solution

dv/dt = -10cm^3/min
dp/dt = ?
equation: PV=c
derivative:
dp/dt x dv/dt = 0

The above isn't right. It is not true that d/dt(PV) = dP/dt * dV/dt. You need to use the product rule.

dp/dt = -dv/dt

but i know what I am doing isn't right. can anyone help me? THANKS!

After you differentiate PV, solve algebraically for dP/dt, and then substitute the values you have.