# algebra

A can do certain task in 8 hours, B in 10 hours and C in 12 hours. How long will it take to do the task if A and B work 1 hour and then A and C finish the task?

1. 3
1. rateA&B=1/10+1/8=18/80=9/40
rateA&c=1/8 +1/12=20/72=10/36

A. How much of the task is done in the first hour?
rate*time=9/40*1=9/40
then how long after the first hour?
time=amountoftaskLeft/rate=(31/40)/(10/36)= 36*31/40*10=2.79 hours more
how long= 1+2.79 hours

posted by bobpursley
2. Task = rate x time , let Task = 1

A's rate = 1/8
B's rate = 1/10
C's rate = 1/12
combined rate of A and B = 1/8+1/10 = 9/40
combined rate of A and C = 1/8 + 1/12 = 5/24
let the total time takens to do the job be x hrs
1(9/40) + (x-1)(5/24) = 1
multiply each term by 120
27 + 25(x-1) = 120
25x - 25 = 93
25x = 118
x = 4.72 hrs or 4 hours and appr 43 minutes

posted by Reiny
3. reiny is correct, my rate for AandC has an error.

posted by bobpursley
4. noted

posted by Melvin

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