AboutAbe Mantell Expertise Hello,
I am a college professor of mathematics and regularly teach all levels
from elementary mathematics through differential equations, and would
be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Expert: Abe Mantell Date: 7/8/2008 Subject: Related Rates
Question Hi, I am having a problem solving a related rates problem.
The height of a rectangular box is 10 inches. Its length increases at a rate of 2 in/sec and its width decreases at the rate of 4 in/sec. When the length is 8inches and the width is 6 inches, the volume of the box is changing atthe rate of?
do i want to use the relation V=lwh?
i set up:
dV/dt to be found
dw/dt = -4
dl/dt = 2
is there a dh/dt and how do i find that if i am already looking for dV/dt?
I'm lost...any help is appreciated! Thankyou.
Answer Hello Stephanie,
Since h is constant, dh/dt=0 and no need to treat h as a variable.
So, V=L*W*10 or V=10LW...now differentiate w.r.t. "t"...
==> dV/dt= 10(L*dW/dt + dL/dt*W), product rule since both L & W are
functions of time (t). Now substitute L=8, W=6, dL/dt=2, dW/dt=-4
==> dV/dt=10[8*(-4) + 2*6]=-200
So the volume is decreasing at the rate of 200 in^3/min.
