1) The last Friday of a particular month is on the 25th day of the month. What day of the week is the first day of the month?
2) Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are opened at the same time, how long will it take to fill the pool? 3) Suppose two days ago was Sunday. What day of the week will 365 days from today then be?
Solutions 1) Three weeks or 21 days before Friday the 25th is Friday the 4th. Count back to the first day. The first day of the month is Tuesday. 2) In one hour, the first pipe will fill 1/8 of the pool, the second pipe 1/12, and the third pipe 1/24. Together, in one hour, they will fill 1/8 + 1/12 + 1/24 or 3/24 + 2/24 + 1/24 = 6/24 = 1/4 of the pool. Therefore, the three pipes will fill the entire pool in 4 hours. 3) Today is Tuesday. 365 days from now is equivalent to 52 weeks and 1 day. 52 weeks from today is also Tuesday. The 365th day is Wednesday