what are the steps to solving this word problem?

Question

Stephanie and Kaylee can finish apiece of work in 5 11/30 days. Stephanie can do the job herself in seven days. If Kaylee wanted to do the job alone, how long would it take her?
Answer :23 days

Answer 1

if Stephanie can do it all in 7 days, then in 5 11/30 days she's done (5 11/30) / 7 = 161/210 = 23/30 of the job, so in that time Kaylee's done 7/30 of it. look at that 1st equation: time worked / time to do it alone = fraction of the job. Let K = time for Kaylee to do it all alone. then (161/30) / K = 7/30, 161/K = 7, K = 161/7 = 23 days.

all of these work problems fit a pattern:
[time #1 worked / time #1 alone] + [time #2 worked / time #2 alone] = 1