Forward Rate Implied by a Target Expected Hitting Time

A CTMC has states 0,1,2 with state 2 absorbing. The rates are a=2 from 0 to 1 and c=1 from 1 back to 0, while the rate from 1 to 2 is b. If the expected time to hit state 2 from state 0 is 1.5, what is b?