let

g = the hours Gigi needs to finish the job alone thus his rate is 100/g letters per hour

a = the hours Abet needs to finish the job alone thus his rate is 100/a letters per hour

Gigi can type 100 letters in 1.2 hours less than Abet

g = a - 1.2

together they finish the job in 1.8 hours thus their together rate is 100/1.8 letters per hour

100/g + 100/a = 100/1.8

plug g = a - 1.2 into the last equation

100/(a - 1.2) + 100/a = 100/1.8

by solving we find

a = 4.297 hr

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g = 4.297 - 1.2

g = 3.097 hr

Gigi needs 3.097 hours to finish the job alone.

Abet needs 4.297 to finish the job alone.