A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days.He was then joined by B.Find the total time taken to finish the work.
A work/day = 1/16
B work/day = 1/12
2(1/16) + x(1/16 +1/12) = 1
8 days
To find the total time taken to finish the work, we need to determine how much work A can complete in one day and how much work B can complete in one day. Then we can calculate the time it takes for them to finish the work when working together.
Let's start by finding the work completed by A in one day. If A can finish the work in 16 days, then in one day, A can complete 1/16th of the work.
Next, let's find the work completed by B in one day. If B can finish the work in 12 days, then in one day, B can complete 1/12th of the work.
Since A worked for 2 days, he completed 2/16th or 1/8th of the work.
When A and B work together, their combined work rate is the sum of their individual work rates. So, the combined work rate of A and B is (1/16 + 1/12).
To find the time taken to finish the work when A and B work together, we can divide the remaining work (7/8) by their combined work rate ((1/16 + 1/12)):
(7/8) / (1/16 + 1/12) = (7/8) / (3/48 + 4/48) = (7/8) / (7/48) = (7/8) * (48/7) = 6 days
Therefore, the total time taken to finish the work when A and B work together is 6 days.