Quadradic word problem help

[rockman64]

Hey Guys! I was going through my math review and am stuck on this problem. Please help as i have a test at 10 am central.

You and your cousin are walking through the lunchroom when you both trip. Your trays hit the ground and both lunches fly through the air in parabolic paths until they hit your friend on the top of the head. If your lunches had not landed on your friend’s head, then your hamburger would have landed on the floor 12 feet away and your cousin’s chili would have landed 16 feet away. Your hamburger reaches a height of 12 feet and your cousin’s chili reaches a height of 6 feet. How tall is your friend?

 

[tkhunny]

You'll certainly have to draw a picture. Let's see it.

Note: Things are unlikely to hit the TOP of a head on the way up. Among other things, this MUST mean your friend is less than 6 ft tall. Why?

 

[skeeter]

burger path no hit ...
starts at (0,0), vertex position (6,12) , and lands (12,0)

chili path no hit ...
starts at (0,0), vertex at (8,6) , and lands at (16,0)

determine an equation for both, then determine their intersection past the launch point