Time-work questions become easy with one idea: rates add. If A finishes a job in 10 days, A does 1/10 of the job per day. If B does 1/15 per day, together they do 1/10 + 1/15 = 1/6 per day, so the job takes 6 days. Never add the days; add the daily rates.
Worked example: A fills a tank in 6 hours and a leak empties it in 8 hours. With both open, the net rate is 1/6 - 1/8 = 1/24 of the tank per hour, so the tank fills in 24 hours. A leak subtracts rate; a helper adds it.