the rate of x is 1/3 job per hour

the rate of y is 1/6 job per hour

let t be the number of hours they work

t = 2k, where k is integer

k (1/3 + 1/6) = 1

k (1/2) = 1

k = 2

t = 2*2 = 4 hours

t = 2k + 1, k is integer

(k+1) (1/3) + k(1/6) = 1

by solving we find

k = 4/3 not integer thus is not solution

click here to see the step by step solution of the equation

indeed in 4 hours

x will for 2 hours and y will work 2 hours and finish the job:

2(1/3) + 2(1/6) = 1

the job will be completed in 4 hours.