A Brass Rod Is 69 $0 ^ { \circ } \mathrm { C }$

A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of $0 ^ { \circ } \mathrm { C }$ The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (brass) and } 2.4 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (aluminum) . }$

A) $510 ^ { \circ } \mathrm { C }$
B) $470 ^ { \circ } \mathrm { C }$
C) $440 ^ { \circ } \mathrm { C }$
D) $490 ^ { \circ } \mathrm { C }$
E) $420 ^ { \circ } \mathrm { C }$