A may complete a work in 90 days,A and B complete the work in 60 days in how many days B alone may complete.?

Question

PLZ TELL ME HOW TO SOLVE THESE TYPE OF PROBLEMS................

Answer 1

Hi,

The general formula is:

A&B..... .....A&B
together.....together
-----------.+.-------------=.1
A alone.....B.alone

For this problem,the formula would be:

60......60
----.+.----- = 1
90.......x

You can reduce the first fraction to give:

2.....60
--.+.---- = 1
3......x

To solve, multiply every term by the LCD, 3x.

2(3x).....60(3x)
--------.+.-------- = 1(3x)
....3............x

This cancels out the fractions and gives the equation:

2x + 180 = 3x

Solving for x,

180 = x

This means person B would need 180 days working alone.

I hope that helps!! :-)

Answer 2

sum of reciprocals:

1/C = 1/A + 1/B or C = 1/ (1/A + 1/B) The same will hold true for any number of people working on the job:

C = 1/ ( 1/X + 1/Y + 1/Z etc- etc)

Where C equals total time it takes A and B working together to do the job.

To find out how long it takes B working alone to do the done solve for B: you use the sum of the reciprocals of the the reciprocals

So if it take A 90 days to do the work by himself and it only takes them 60 days if A and B are working together.
The question is how long it will take B to complete the work if he is working by himself.?

The basic formula is this!

1/C = 1/A + 1/B
your unknown is B so you are going to have to get it by itself on one side of the equation in order to solve for it.

First thing is subtract both sides by 1/C

1/C - 1/C = 1/A + 1/B - 1/C
collect your terms (simplify)

0 = 1/A + 1/B - 1/C
now isolate B on one side of the equation. rarranging terms first.
0 = 1/B + (1/A - 1/C)
subtract both sides by (1/A - 1/C)

0 - (1/A - 1/C) = 1/B + (1/A -1/C) -(1/A -1/C)
this gives you!
-(1/A - 1/C) = 1/B
clear the paranthesis: since it is - (1/A - 1/C) multiply by -1 which gives you - 1/A + 1/C

- 1/A + 1/C = 1/B

Plug in your numbers:

- 1/90 + 1/60 = 1/B
you can do this two ways first way if your are not using a scientific calcuator. you have to find a common denomiator. which will be 180

- 2/180 + 3/180 = 1/B

which comes out to:
1/180 = 1/B

now take the reciporcals of both sides:

1/ (1/180) = 1/ (1/B)
which gives you.

B = 180

If you are using a sci calculator you can do it this way.

1/B = - (1/A - 1/C)
take reciporcal of both sides.
B = 1/ - (1/A - 1/C)
B= 1/ - (1/A -1/C)
clear paranthesis
B = 1/ - 1/A + 1/C

B= 1/ -1/90 + 1/60

Way to work it on calculator.
using {| |} to show keys on calculator. Note x-1 key can also be shown 1/x key and the - key can also be shown as +/- depending on calculator: I was using a Ti 84: and Fx 70000 Casio:

{| - |} 90 {|x-1|} {|+|} 60 {|x-1|} {|=|} {|x-1|} {|=|} your ans.

On a less expensive calcualator with the +/- key you have to work it this way:

90 {| +/- |} {| 1/x|} + 60 {| 1/x |} {|=|} {| 1/x|} {| = |} your answer:

Several one trick you need to know is if they are equal then you simply divid by the number doing the job.

A can do the job in 60 hour and B can do the job in 60 hours how long will it take them working together to get job done?

in this case since A = 60 and B = 60 you simply divide by 2

so total time for the two of them will be 60/2 = 30 hours

Ok if you have 3 people doing the job and A can do the job in 60 B can also do the job in 60 and C can also do the job in 60 hours you simply divide by 3
so total time for the three of them working together to get the job done will be 60/3 = 20 hours to get job done:

But this only holds true if they are all equal.

The advantage of using the reciporical method is it is a lot easier when working with more than two people. or two knowns such as resistors in parallel when analysing a circuit.

Also works of water lines in parallel:

another method that work with just two is the product over sum method:

C = A*B / (A + B)
But is harder to rewrite and simplify to find either A or B:

Answer 3

"A may complete a work in 90 days"
means
rate of working (of A) = 1/90
Rate (A) = 1/90

A and B complete the work in 60 days
Rate of working (of A, B) = 1/60
Rate(A) + Rate(B) = 1/60

so,
rate (B) = 1/60 - rate (A)
Rate(B) = 1/60 - 1/90 = 1/180

so, B alone will take 180 days

Answer 4

A's one day work = 1/90
A & B' s one day work = 1/60
Therefore B's one day work = 1/60 - 1/90 = 1/180
B's will complete the work in 180 days

Answer 5

30

Answer 6

180 days...i
A's one day work =1/90 as per question
A+B's one day work= 1/A+1/B
1/A+1/B=1/60
1/B=1/60-1/90
therfore 1/B=1/180
B=180 days