CPM Homework Help : APCALC Problem 11-26

Multiple Choice: A $4$ -foot tall child walks away from a $12$ -foot tall street light at a rate of $2$ ft/sec. At what rate is the length of her shadow increasing when she is $6$ feet away from the light?

$1$ ft/sec

$2$ ft/sec

$3$ ft/sec

$4$ ft/sec

$6$ ft/sec

Hint:

Sketch the situation. Your sketch should have similar right triangles.

Step:

If the child's distance from the light is $d$ and their shadow length is $s$ , then:

$\frac{12}{s+d}=\frac{4}{s}$

Step:

The equation can be rewritten as $2s = d$ .
Now differentiate.

Step:

$2\frac{ds}{dt}=\frac{dd}{dt}$

Now use the information given in the problem to solve for $ds/dt$ .