Page 64 - How To Solve Word Problems In Calculus

Step2
dx
Given: = 30,
dt

dy
=−20 ← dy/dt is negative since y is shrinking.
dt dy
If we take = 20, we will get an in-
dt
correct answer.
dz
Find: 1 hour later
dt

Step3
2
2
z = x + y 2
Step4
dz dx dy
2z = 2x + 2y
dt dt dt
dz dx dy
z = x + y
dt dt dt

Step5
After 1 hour, x = 30 miles and
Distance = rate × time
y = 60 − 20 = 40 miles.

2
z = x + y 2
√
= 900 + 1600 = 50 miles
From step 4

dz
50 = 30 · 30 + 40(−20)
dt
dz
50 = 100
dt

dz
= 2
dt

The distance between the cars is increasing at the rate of
2 mi/h.

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