SOLUTION: A 6-foot man, standing in front of a 15-foot lamppost, casts a shadow of 8 feet. If he steps another 3 feet away from the lamppost, how much will his shadow lengthen?
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Question 1152309: A 6-foot man, standing in front of a 15-foot lamppost, casts a shadow of 8 feet. If he steps another 3 feet away from the lamppost, how much will his shadow lengthen?
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The man and his shadow are 6 and 8 feet
The lamp and the total shadow of the lamp is 15 and x feet.
This is a proportion, and the shadow of the lamp is 20 feet, and the distance the man is from the lamp is 20 feet - his shadow or 12 feet
When the man steps further away, he is still 6 feet and the lamp still is 15 feet.
The man's shadow is x feet long and he is 15 feet from the lamp.
The lamp's shadow is therefore x+15 feet
so the proportion is 6/15=x/(x+15)
This is 6x+90=15x
9x=90
x=10 feet, man's shadow.
It lengthened 2 feet.
