Law cosines:

16 + 256 - 128

=> y ≈ 16.51;
Law sines: 16/sinx = 16.51/sin30 => sinx = 0.48 => x ≈ 29 degrees;
Let x be the amount invested at 6%
840 = 0.06x + 0.075(2x)
840 = 0.06x + 0.15x
840 = 0.21x
x = 840/0.21
x = 4000
Therefore, she invests $4000 at 6% and $8000 at 7.5%
The approximate difference between these average distances is 330 kilometers
The time taken to paint the whole room would be six times the time taken to paint 1/6 of her room:

The answer is: 14.4 hours.