algebra math im so confused

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 10 feet.

Answer 1

using algebra...

A+B=2178

A-B=10

A=B+10

B+10+B=2178

2B=2168

B=1084 feet

A=1094 feet

using arithmetic...

2178/2=1089

1089 and 1089 no

1090 and 1088 no

1091 and 1087 no

1092 and 1086 no

1093 and 1085 no

1094 and 1084 yes