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By the 5th day, Shirley will have saved $50

To catch up, Farah needs to save for 10 days.

To verify that this is correct, we calculate how much both of them saved on the 15th day.

(Shirley) 10 x 15 = 150

(Farah, starts 5 days later than Shirley) 15 x 10 = 150

We see that Farah needs to save for 10 days to catch up.