Using two significant figures and 3,600 seconds per hour:
3000' ≈ .49 nm
7000' ≈ 1.2 nm
GS ≈ 200 kt
Time in seconds over horizontal 3000' ≈ 0.49 / 200 x 3600 ≈ 8.8
Speed over vertical 7000' ≈ 1.2 / 8.8 x 3600 ≈ 490
Speed down slope ≈ (200^2 + 490^2)^½ ≈ 530 kt
The structural failure may have happened before achieving this speed.