Page 63 - How To Solve Word Problems In Calculus

accomplished by using the equation obtained in step 3.

2
2
x + y = 20 2
2
2
12 + y = 20 2 If you recognize a 12-16-20 right
triangle, this calculation is un-
2
144 + y = 400 necessary.
2
y = 256
y = 16
Substituting into the equation obtained in step 4, we obtain

dy
12 · 1 + 16 = 0
dt
dy
16 =−12
dt

dy 3
=−
dt 4
The negative derivative means that y is decreasing. The top of
3
the ladder is falling at the rate of ft/sec.
4
EXAMPLE 5
At a certain instant, car A is 60 miles north of car B. A is
traveling south at a rate of 20 mi/h while B is traveling east
at 30 mi/h. How fast is the distance between them changing
1 hour later?
Solution
Step1

A

A
60
z
y

B
x B

50