Sarah and Rehema working together can complete a piece of work in 6 days while Sarah working alone can complete work in 10 days . The two worked together for 3 days and Sarah withdrew . Find time taken by Rehema to complete the remaining work.
Let's calculate the rate at which Sarah can complete work alone.
Since Sarah can complete the work alone in 10 days, then her work rate is 1/10.
Let's calculate the rate at which Sarah and Rehema can complete work together.
Sarah and Rehema can complete work together in 6 days, so their joint work rate is 1/6.
If they worked together for 3 days, then they completed 3 * (1/6) = 1/2 of the work.
Since Sarah can complete 1/10 of the work alone in a day, then in 3 days she can complete 3 * (1/10) = 3/10 of the work.
Therefore, Rehema was left to complete 1/2 - 3/10 = 5/10 - 3/10 = 2/10 = 1/5 of the work.
Since Rehema is completing 1/5 of the work, it will take her 5 * 6 = <<5*6=30>>30 days to complete the remaining work.
Therefore, Rehema will need 30 days to complete the remaining work.