Question

There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 2178 feet, while the difference of their lengths is only 14 feet.Find the length of each carrier

Answer 1

This is a system of two equations with two unknowns

`\begin{gathered} A+B=2178 \\ A-B=14 \end{gathered}`

Solve for A (or B) in one of the two equations and plug it into the other. For example,

`\begin{gathered} A-B=14 \\ A=10+B \end{gathered}`
`\begin{gathered} A+B=2178 \\ (10+B)+B=2178 \\ 10+2B=2178 \\ 2B=2178-14 \\ 2B=2164 \\ B=(2164)/(2) \\ B=1082 \\ \end{gathered}`

Now,

`\begin{gathered} A=10+B \\ A=10+1082 \\ A=1092 \end{gathered}`

Carrier A = 1092 feet

Carrier B = 1082 feet