A and B can finsih a 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's rate = 1/16
B's rate = 1/12
combined rate = 1/16+1/12 = 7/48
let the total time taken be t days
so ...
2(1/16) + (t-2)(7/48) = 1
1/8 + (7/48)t - 7/24 = 1 , ----- 1 for whole job
7t/48 = 1 - 1/8 + 7/24
7t/48 = 7/6
7t = 56
t = 8 days
So it took 8 days, with A working alone for 2 days, then 6 more with both working.
check:
so A worked for 2 hrs
then A and B worked together for 6 more hours
so 2(1/16) + 6(7/48)
= 1/8 + 42/48
= 1