If he purchases the Yorkville bond:

Portfolio duration = (w₁ × ED₁) + (w₂ × ED₂)
Portfolio duration = ((840 / 900) × 10.315) + ((60 / 900) × 8.51)
Portfolio duration = (0.933 × 10.315) + (0.067 × 8.51)
Portfolio duration = 9.624 + 0.570
Portfolio duration = 10.194

If he purchases the Mountain States bond:

Portfolio duration = (w₁ × ED₁) + (w₂ × ED₂)
Portfolio duration = ((840 / 900) × 10.315) + ((60 / 900) × 6.30)
Portfolio duration = (0.933 × 10.315) + (0.067 × 6.30)
Portfolio duration = 9.624 + 0.422
Portfolio duration = 10.046

Note, however, that we did not need to calculate the duration of the portfolio if he purchases the Yorkville bond. Since we know that the Mountain States bond has lower effective duration than the Yorkville bond, we know that the lowest effective duration for the total portfolio would be achieved by investing all $60 million in the Mountain States bond.