# 08-09 Rate of movement of shadow on the ground

**Problem 08**

A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast does the end of his shadow move?

**Solution 08**

$\dfrac{s - x}{6} = \dfrac{s}{16}$

$16s - 16x = 6s$

$10s = 16x$

$10\dfrac{ds}{dt} = 16\dfrac{dx}{dt}$

$10\dfrac{ds}{dt} = 16(5)$

$\dfrac{ds}{dt} = 8 \, \text{ mi/hr}$ *answer*

**Problem 09**

In Problem 08, how fast does the shadow lengthen?

**Solution 09**

$\dfrac{s}{6} = \dfrac{s + x}{16}$

$16s = 6x + 6s$

$10s = 6x$

$10\dfrac{ds}{dt} = 6\dfrac{dx}{dt}$

$10\dfrac{ds}{dt} = 6(5)$

$\dfrac{ds}{dt} = 3 \, \text{ mi/hr}$ *answer*

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