Two workers, if they were working together, could finish a certain job in 12 days. If one of the workers does the first half of the job and then the other one does the second half, the job will take them 25 days. How long would it take each worker to do the entire job by himself?
it would take 40 days and 60 days
To solve this problem, we need to use the concept of work rates. Let's assume that worker A can complete the job in x days, and worker B can complete the job in y days.
Given that two workers working together can finish the job in 12 days, we can say that their combined work rate is 1/12 of the job per day. This can be expressed as:
1/x + 1/y = 1/12 -- Equation 1
Now, let's consider the scenario where worker A completes the first half of the job and worker B completes the second half in 25 days. In this case, if worker A completes half the job in x days, their work rate would be 1/(2x) of the job per day. Similarly, if worker B completes the other half in y days, their work rate would be 1/(2y) of the job per day. Combining the two work rates, we get:
1/(2x) + 1/(2y) = 1/25 -- Equation 2
We have a system of two equations with two unknowns (x and y). We can solve this system to find the values of x and y, which represent the number of days each worker would take to complete the entire job individually.
To solve the equations, we can first simplify Equation 1 by multiplying both sides by 12xy:
12y + 12x = xy -- Equation 3
Next, simplify Equation 2 by multiplying both sides by 50xy:
25y + 25x = xy -- Equation 4
Now, we can rearrange Equation 3 to solve for y:
12y = xy - 12x
12y = x(y - 12)
y = x(y - 12)/12
Substitute this value of y into Equation 4:
25(x(y - 12)/12) + 25x = xy
25xy - 300x + 300x = 12xy
25xy - 12xy = 300x
13xy = 300x
Dividing both sides by 300x, we get:
13y = 300
y = 300/13
Therefore, worker B would take 300/13 days to complete the job by himself.
To find the value of x, we substitute the value of y into Equation 3:
12(300/13) + 12x = x(300/13)
3600/13 + 12x = 300x/13
3600 + 156x = 300x
3600 = 144x
x = 3600/144
Therefore, worker A would take 3600/144 = 25 days to complete the job by himself.
In summary, worker A would take 25 days and worker B would take approximately 23.08 days to complete the entire job individually.
110
Two workers, if they were working together, could finish a certain job in 12 days. If one of the workers does the first half of the job and then the other one does the second half, the job will take them 25 days. How long would it take each worker to do the entire job by himself?
Answer
Its 20 and 30
combined rate=job/12days
rate1=.5job/Time1
rate2=.5job/(25-time1)
rate=rate1+rate2
job/12=.5job/time1+.5job/(25-time1)
looking for time1 t.
t(25-t)=6(25-t)+6(t)
25t-t^2-150=0
t^2-25t+150
(t-10)(t-15)=0
t=10, 15
and if you look at the second worker, time=25-t...
so the two workers can finish in 10 hours for one, 15hours for the other.