Related
Rate
Example
Problems
1.
Air
is
being
pumped
into
a
spherical
balloon
at
a
rate
of
100
cm3/s.
How
fast
is
the
radius
of
the
balloon
increasing
when
its
diameter
is
50cm?
2.
A
ladder
10ft
long
rests
against
a
vertical
wall.
If
the
bottom
of
the
ladder
slides
away
from
the
wall
at
a
rate
of
1ft/s,
how
quickly
is
the
top
of
the
ladder
moving
when
the
base
of
ladder
is
6ft
from
the
wall?
3.
A
water
tank
has
the
shape
of
an
inverted
cone
whose
height
is
always
twice
its
radius.
The
tank
is
being
filled
with
water
at
a
rate
of
2m3/min.
Find
the
rate
at
which
the
water
level
is
rising
when
it
is
3m
deep.
4.
A
man
is
walking
along
a
straight
path
at
a
speed
of
4ft/s.
A
searchlight
is
located
on
the
ground
20ft
from
the
path
and
is
kept
focused
on
the
man.
At
what
rate
is
the
searchlight
rotating
when
the
man
is
15ft
from
the
point
on
the
path
closest
to
the
searchlight?
5.
A
man
starts
walking
north
at
4ft/s
from
a
point
P.
Five
minutes
later
a
woman
starts
walking
south
at
5ft/s
from
a
point
500ft
due
east
of
P.
At
what
rate
is
the
distance
between
them
increasing
15
minutes
after
the
woman
starts
walking?
6.
At
noon,
ship
A
is
100km
due
west
of
ship
B.
Ship
A
is
sailing
south
at
35km/hr
and
ship
B
is
sailing
west
at
25km/hr.
How
fast
is
the
distance
between
them
changing
at
3:00p.m?
7.
A
highway
patrol
plane
flies
1
mile
above
a
straight
stretch
of
road
at
a
steady
speed
of
100mph.
The
pilot
sees
an
oncoming
car
and,
with
radar,
determines
the
distance
between
the
plane
and
the
car
is
1.8
miles
and
is
decreasing
at
a
rate
of
140mph.
Is
the
car
speeding?
(The
limit
on
this
stretch
is
60mph.)
8.
A
Ferris
wheel,
40
feet
in
diameter,
revolves
at
a
rate
of
8
radians
per
minute.
How
fast
is
a
passenger
rising
when
(s)he
is
12
feet
higher
than
the
center
of
the
Ferris
wheel
and
rising?