+129899 Let the portion of the job that Alice can complete in one hr = 1/ x
Let the portion of the job that Bob can complete in one hr =1/ y
Let the portion of the job that Charlie can complete in one hr = 1/ z
So we have this system
2 [ 1/x + 1/y] = 1 ⇒ 1/x + 1/y = 1/2 (1)
3 [ 1/x + 1/z ] = 1 ⇒ 1/x + 1/z = 1/3 (2)
4[ 1/y + 1/z] = 1 ⇒ 1/z + 1/y = 1/4 (3)
Subtract (3) from (1) ⇒ 1/x - 1/z = 1/4 ( 4)
Add (2) + (4) = 2/x = 7/12 ⇒ 1/x = 7/24
Using (1) to find y, we have that
1/y = `1/2 - 7/24 = 5/24
And using (3) to find 1/z we have
1/z = 1/4 - 5/24 = 6/24 - 5/24 = 1/24
So.....Alice completes 7/24 of the job in an hour......Bob completes 5/24 of the job in an hour and Charlie completes 1/24 of the job in an hour
Add these and take the reciprocal = [7 + 5 + 1 ] / 24 = 13/24
So.......they take 24/13 hrs ≈ 1.846 hrs to complete the job working together
