let

x = the hours the old computer need to complete the calculation by itself, x>0

y = the hours the new computer need to complete the calculation by itself, y>0

A new computer can complete a complex biochemistry calculation in 11 hours less than an older-model computer:

y = x - 11

x = y + 11

Working together, the new computer and the old computer can complete the calculation in 18 hours:

the rate of the old computer + the rate of the new computer = the together rate per hour that is 1/18 calculation per hour

1/x + 1/y = 1/18

plug x = y + 11 into the last equation:

1/(y + 11) + 1/y = 1/18

by solving we find:

y = 31.3 hr

click here to see the step by step solution of the equation:

the new computer can complete the calculation by itself in 31.3 hours.