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?
Hana can do a certain task in 8 hours, Beth in 10 hours, and Camille in 12 hours. How long will it take to do the task if Hana and Beth work 2 hours and then Hana and Camille finish the task?
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
reiny is correct, my rate for AandC has an error.
noted
Plss help ms
To find out how long it will take for both A and B to work together for 1 hour, we need to calculate their combined work rate.
A can complete the task in 8 hours, so their work rate is 1 task / 8 hours = 1/8 task per hour.
Similarly, B can complete the task in 10 hours, so their work rate is 1 task / 10 hours = 1/10 task per hour.
To find their combined work rate, we add these two rates together:
1/8 task per hour + 1/10 task per hour = 10/80 + 8/80 = 18/80 task per hour = 9/40 task per hour.
Since A and B work together for 1 hour, the amount of work they complete is (1/40) of the task.
Next, A and C finish the task. We need to calculate their combined work rate.
A's work rate is still 1/8 task per hour, and C can complete the task in 12 hours, so their work rate is 1/12 task per hour.
Adding these two rates together gives us:
1/8 task per hour + 1/12 task per hour = 3/24 + 2/24 = 5/24 task per hour.
Since A and C work together to finish the remaining task, the time it takes for them to complete the remaining task is the reciprocal of their combined work rate:
24/5 hours.
Therefore, it will take A and B 1 hour and A and C an additional 24/5 hours to finish the task.
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