KCC's Quizzes AQQ267 on job execution timing

Let:  W is the total amount of work to be done
        A, B and C  the "speed" ( work done per hour)
We have  2(A+B)  = W  or   A+B  = W/2
                                            A+C  = W/3
                                            B+C =  W/4
3 linear equations with 3 unknowns.
Solution is A = (7/24) W,  B=(5/24)W and C = (1/24)W.  All are positive, ok. Checking the originale eq.  ... ok.

A+B+C = (13/24)W,  so it will take them 24/13 hours to complete 1 W. ( A little bit less than 2 hours, which is less than A+B alone)

Annie=A, Bruce=B, Carrie=C

Then 1/A + 1/B = 1/2  and 1/B + 1/C = 1/3 and 1/B + 1/C = 1/4.

--> 2*( 1/A + 1/B +1/C) = 1/2 + 1/3 +1/4 = 13/12

--> (1/A + 1/B +1/C) = 13/24

-->  24/13 days when all three works together

Answer is 24/13 of an hour (a bit less than 2 hours).

Be A, B and C the rate of working of Annie, Bruce and Carlos. You can write

A+B=1/2

A+C=1/3

B+C=1/4

You get 

A=7/24, B=5/24, C=1/24

So the total rate of working is 13/24 and from this you get the result.

Progress P(t)= (annie's rate + bruce's rate + carlos' rate) * t

System of equations:

2A + 2B = 1

3A + 3C = 1

4B + 4C = 1

Solve the system to get A = 7/24, B = 5/24, C = 1/24

t = P / (A+B+C) = 24/13 = 1.85 hours or 1 hour 51 min

Excellent vanderghast , you get it, congratulations!

Bingo hunl , right answer, congratulations!

Bravo gpiarino , right answer with clear development!

YES! You get it Kolibrimann , congratulations!

Let T be the task quantity that the three workers are producing.  This establishes three equations where the Ar, Br, and Cr are the worker time rates of production.

2Ar+2Br+0 = T

3Ar+0+3Cr = T

0+4Br+4Cr = T

Solving these equations gives:

Ar=7T/24

Br=5T/24

Cr=T/24

When all three work together to produce T, it’s done in time t.

tAr+tBr+tCr = T

(7+5+1)t = 24

t = 1.846 hours to produce T when all three work together.

Taking Annie as A, Bruce as B, and Carlos as C;

and work done = 1/time so,

1/A + 1/B = 1/2
1/A + 1/C = 1/3
1/B + 1/C = 1/4

adding all equations gives ==> 2 ( 1/A + 1/B + 1/C ) = 13/24

==> A + B + C = 1.846 which is approx 1.85 hours