If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

(A) 0.8 days
(B) 1.09 days
(C) 1.23 days
(D) 1.65 days

Question

If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

(A) 0.8 days
(B) 1.09 days
(C) 1.23 days
(D) 1.65 days

hero · Answer

Let
s = Number of Days Sam Does A Job
l = Number of Days Lisa Does A Job
t = Number of Days Tom Does A Job

Then:
$$\frac{slt}{sl + st + lt}$$

hero · Answer

In other words, 

Number of days then do it together is:

$$\frac{4 \dot\ 6 \dot\ 2}{(4)(6) + (4)(2) + (6)(2)}$$

raden · Answer

v1+v2+v3 = x/4 + x/6 + x/2
v1+v2+v3 = (3x+2x+6x)/12
v1+v2+v3 = 11x/12
v1+v2+v3 = x/(12/11)
so, if they are do it together for 12/11 = 1.09

raden · Answer

just same like @Hero

hero · Answer

Mines is simpler bro

raden · Answer

yea, i see...