1550.14 – Toy Rocket

A toy rocket is lying on its side in the middle of Tappan Square ready to be raised up for launch. The rocket has three sections. Section C, the top of the three sections, is 22 cm tall. Section B, the middle section, is as tall as Stage C plus half the height of Stage A. Stage A, the bottommost section, is as tall as Stages B and C combined.

How tall is the toy rocket in its entirety?

Solution

We are given the following information:

C=22B=C+A2A=B+C\begin{aligned}C &= 22 \\B &= C + \dfrac{A}{2} \\A &= B + C\end{aligned}

We begin using the fact that C=22C = 22:

B=22+A2A=B+22,soB=A−22\begin{aligned}B &= 22 + \dfrac{A}{2} \\A &= B + 22, \hspace{.1in} \text{so} \\B &= A - 22\end{aligned}

Now we equate the two equations for B:

22+A2=A−2244=A−A2,therefore A=88\begin{aligned}22 + \dfrac{A}{2} &= A - 22 \\44 &= A - \dfrac{A}{2}, \hspace{.1in} \\\text{therefore } A &= 88\end{aligned}

Knowing the values for Sections AA and CC, we can easily find that B=66B = 66. So, the total height of the toy rocket is 176cm. That's about 5 feet 10 inches.