Problema Solution
two workers A & B together could finish a work in 8 days. they work together for 6 days and A left. remaining work was finished by B alone in 6 days. how many days individually each would have taken to finish the work?
Answer provided by our tutors
let
a = the time in days that A needs to finish the job alone
the rate of A per day is: 1/a work/day
b = the time in days that B needs to finish the job alone
the rate of B per day is: 1/b work/day
two workers A & B together could finish a work in 8 days means that hey together rate per day is: 1/8 work/day
thus we can write:
1/a + 1/b = 1/8
they work together for 6 days and A left
this means 6/8 of the job was done
what is remaining is 1 - 6/8 = 2/8 = 1/4 of the job
B finished the remaining 1/4 of the job alone in 6 days, this means:
6(1/b) = 1/4
by solving we find:
b = 24 days
click here to see the step by step solution of the equation:
B needs 24 days to finish the job alone.
Using 1/a + 1/b = 1/8 and plugging b = 24 we find a:
1/a + 1/24 = 1/8
by solving we find:
a = 12 days
click here to see the step by step solution of the equation:
A needs 12 days to finish the job alone.