How Tall is Harold? Systems of Quadratics Task

I worked through the How Tall is Harold? quadratics task from CPM’s Algebra 2 Connections Curriculum at a 2013 Common Core Workshop I attended (OGAP).

I am blogging about the activities we did last summer so that they are easier for me to find when I go to plan lessons. I hope these ideas will inspire you as well.

How Tall is Harold?

Jamal and Dinah were still eating as they came into Algebra 2 class from lunch. Someone had left a book on the floor and they tripped. As they each hit the floor, the food they were carrying went flying across the room directly toward Harold, who was showing off his latest dance moves.

As Jamal and Dinah watched in horror, Jamal’s cupcake and Dinah’s sandwich splattered Harold right on top of his head! Jamal’s cupcake flew on a path that would have landed on the floor 20 feet away from him if it had not hit Harold.

Dinah’s sandwich flew on a path that would have landed on the floor 24 feet away from her if it had not hit Harold. Jamal’s cupcake got up to 9 feet high, and Dinah’s sandwich reached a height of 6 feet, before hitting Harold.

How tall is Harold? Show your solution in as many ways as you can.

We ended up setting up a system of equation involving quadratics, but now I’m wondering if there is another way to solve it based on the encouragement to “show your solution in as many ways as you can.”