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Explanation:
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.
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