Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours. How many hours will it take A to finish the work independently?
(1) Working together, A and B can finish the work in 4 hours.
(2) Working together, B and C can finish the work in 48/7 hours.
Please solve this question for me
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jainrahul1985
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PussInBoots
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1/a + 1/b + 1/c = 1 / (8/3)
1/b + 1/c = 1 / (40/7)
Find 1/a, that's rate of work / hour. You'll get 1/5, hence 5 hours
1/b + 1/c = 1 / (40/7)
Find 1/a, that's rate of work / hour. You'll get 1/5, hence 5 hours
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anuragkundargi
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Work is 1 Unit
Let the rate of A= Ra , rate of B = Rb, rate of C= Rc
Combined Rate= Ra+ Rb + Rc
Rate= Work/ Time
Time= Work/ Rate = 1/Ra+ Rb + Rc =8/3
Ra+ Rb + Rc =3/8...............(1)
Also from 2nd statement,
1/Rb + Rc =48/7
Rb + Rc =7/48...........(2)
Substituting (2) in (1), we get
Ra + 7/48= 3/8
Ra=11/48
Time taken by A alone = Work/ Ra
= 1/(11/48)
=48/11
Let the rate of A= Ra , rate of B = Rb, rate of C= Rc
Combined Rate= Ra+ Rb + Rc
Rate= Work/ Time
Time= Work/ Rate = 1/Ra+ Rb + Rc =8/3
Ra+ Rb + Rc =3/8...............(1)
Also from 2nd statement,
1/Rb + Rc =48/7
Rb + Rc =7/48...........(2)
Substituting (2) in (1), we get
Ra + 7/48= 3/8
Ra=11/48
Time taken by A alone = Work/ Ra
= 1/(11/48)
=48/11
