how many days will they take to complete the same job if they work together at the same rate
2006-10-03 04:52:43 · 12 answers · asked by ramsay_sam 1 in Science & Mathematics ➔ Mathematics
The first answer above is right, but I figured I'd add some explanation, since I see these problems often.
If person 1 takes t1 amount of time to complete a job and person 2 takes t2 amount of time to complete the same job, here's how long it takes both working together.
Let x be the fraction of the job that person 1 will do (i.e. 0.5 for half the job), and let t be the amount of time that each will spend when they work together.
Then t=t1*x, because the whole job would take t1.
But since they will work for the same period of time, we also know t=t2*(1-x), because person 2 will be doing the rest of the job.
Therefore, t1*x=t2*(1-x). Solve for x and get
x=t2 / (t1+t2).
As mentioned above, the time needed for both to complete the job is t=t1*x, which gives you
t = t1*t2 / (t1+t2).
Divide the numerator and denominator by t1 and t2 and get the same formula as in the first answer,
t = 1 / (1/t1 + 1/t2).
2006-10-03 05:05:03 · answer #1 · answered by James L 5 · 0⤊ 0⤋
1.416667 days! The father does 1/4 of the job each day. The son does 1/3 of it. The first day, together they do 1/4 + 1/3= 3/12 + 4/12 =7/12. That leaves 5/12 of the job for the next day. 5/12= 0.416666666667. 1 + 0.416667 =1.416667.
2006-10-03 11:59:09 · answer #2 · answered by miyuki & kyojin 7 · 0⤊ 1⤋
Let';s find their rates of doing the work
F: 1/4 job/day
S 1/3 job/day
both working 1/4+1/3 job/day
(1/4 +1/3) t = 1 complete job
7/12 * t = 1
t= 12/7 days = 1 5/7 days
2006-10-03 12:09:03 · answer #3 · answered by rwbblb46 4 · 0⤊ 0⤋
The dad does 1/4 of the job in a day; the son does 1/3; together they do 1/x of the job.
1/4 + 1/3 = 1/x
3/12 + 4/12 = 7/12 = 1/x
x = 12/7 days or 1 5/7 days.
2006-10-03 12:01:58 · answer #4 · answered by hayharbr 7 · 1⤊ 0⤋
1 and 5/12 days
2006-10-03 12:45:31 · answer #5 · answered by Toy 2 · 0⤊ 0⤋
1/4 job in 1 day
1/3 job in 1 day
7/12 job in 1 day
1 job in 12/7 days
1 and 5/7 days
2006-10-03 12:02:28 · answer #6 · answered by bob h 3 · 1⤊ 0⤋
father trusted his son to do the job, while his son think his father would do the job, and after the fourth days they both realize that the job have not been done yet, they decided to work as a team and the job done in 5,4 days hehee
2006-10-03 12:13:01 · answer #7 · answered by morroniac 2 · 0⤊ 0⤋
The formula is easy. (AxB)/(A+B) = 12/7 Days which gives you the 1.714286 days.
2006-10-03 12:02:51 · answer #8 · answered by mrmnguy 1 · 1⤊ 0⤋
3 and a half days surely
2006-10-03 12:01:06 · answer #9 · answered by Gingershiv 3 · 0⤊ 1⤋
1
---------------------
1/4 + 1/3
= 1.714 days
2006-10-03 11:55:26 · answer #10 · answered by davidosterberg1 6 · 1⤊ 0⤋