Answer:
The first worker complete the job in 25 days himself
The second worker complete the job in 20 days himself
Explanation:
r1= rate of work done by first worker
r2=rate of work done by second worker
W= total work done
t days= time taken by the 1st worker to complete the job
r1(t)=W
r1=W/t (1)
Then the time taken by the 2nd worker to complete the job is t-5 days.
r2(t−5)=W
r2=W/(t−5) (2)
If 1st worker do the job for 1 hour and then both the worker do the job for 4 hours and 40% work is done, So
r1(1)+(r1+r2)(4)=4W/10
r1+4r1+4r2=4W/10
5r1+4r2=4W/10 (3)
Substitute equation 1 and 2 into (3)
5W/t+4{W/(t−5)}=4W/10
Multiply through by 10(t-5)
5/t+4/t−5=4/10
5(10)(t−5)+4(10)(t)=4(t−5)(t)
50t−250+40t=4t^2−20t
4t^2−110t+250=0
Solving the above quadratic equation using factorization method
4t^2−100t−10t+250=0
4t(t−25)−10(t−25)=0
(t−25)(4t−10)=0
t=25 or t=2.5
2.5 can't be the answer because if we take 2.5 days in which 1st worker completes the work, then the second worker will complete the work in -2.5days which is wrong.
The first worker completes the job in 25 days by himself and the second worker completes the job in 20 days by himself.
Answer:
ASSUMPTIONS
The work done by the first worker be X
The work done by the second worker be Y
If Z is assumed to be the total work done
Then, the time taken for the 1st worker to complete the job is h days
X(h)=Z--------------------------------equation 1
Then the time taken by the 2nd worker to complete the job is h-5 days.
Y(h-5)=Z-------------------------------equation 2
from equation 1, X=Z/h--------------- equation 3
from equation 2, Y=Z/(h-5)---------- equation 4
worker 1 do the job for 1 hour and then both worker 1&2 do the job for 4 hours and 40% work is done:
X(1) + (X+Y)4= 4Z/10X
X+4X+4Y=4Z/10
5X+4Y=4Z/10-----------------------equation 5
From equation 3, X=Z/h
From equation 4, Y=Z/(h-5)
substituting the value of X and Y in equation 5,
5(Z/h) + 4(Z/(h-5))=4Z/10
5Z/h + 4Z/(h-5)=4Z/10
5/h + 4/(h-5)= 4/10
multiply through by the lowest common factor which is 10(h-5)
we have: 5/h×10(h-5) + 4/(h-5)×10(h-5)= 4/10×10(h-5)
50h - 250 + 40h = 4h² - 20h
4h²-110h+250=0
solving the quadratic equation,
4h²-100h-10h+250=0
4h(h-25) -10(h-25)=0
(4h-10) (h-25)=0
Therefore,
4h-10=0 or h-25=0
4h=10 or h=25
h=10/4 or h= 25
h=2.5 or h=25
2.5 can't be the answer because if we take 2.5 days for the 1st worker to complete the work, then the second worker will complete the work in -2.5days which is wrong.
So, the first worker completes the work in 25 days (h=25) by himself and the second worker completes thework in 20 days (h-5=25-5=20) by himself.
Explanation:
