Original
First, we {{CMD_172}}introduce variables{{CMD_173}} {{MATH_174}}, the distance the plane has traveled after it flew right above you, and {{MATH_175}}, the distance between you and the plane.
The given rate is {{MATH_176}} mph and the unknown rate is {{MATH_177}}, when {{MATH_178}}.
Next, we {{CMD_179}}draw a picture{{CMD_180}}.
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Next we {{CMD_184}}find equations{{CMD_185}} relating the variables {{MATH_186}} and {{MATH_187}}. By the Pythagorean Theorem
we know that
{{MATH_188}}
Since {{MATH_189}} and {{MATH_190}} are functions of time, we now
{{CMD_191}}differentiate{{CMD_192}} both sides of the equation
{{MATH_193}}
At the instant when {{MATH_194}} mi, we get that
{{MATH_195}}
This implies that {{MATH_196}} has to be evaluated at time when {{MATH_197}}. In order to do that,
let's draw the picture at the given instant, when {{MATH_198}} mi.
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