If A works 3 times as fast, he'll do the job in 1/3 the time:
A = (1/3)B
B - A = 60
B - (1/3)B = 60
Multiply through by 3:
3B - B = 180
2B = 180
B = 180/2
B = 90
A = (1/3) * 90
A = 30

So A can do the job in 30 days, so A can do 1/30 of the job per day.
So B can do the job in 90 days, so B can do 1/90 of the job per day.
Working together, they can do (1/30) + (1/90) of the job per day, which is (3/90) + (1/90) = (3 + 1) / 90 = 4/90 =
So the job will take 90/4 days, which is 45/2 or 22.5 days

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