# algebra

posted by melvin

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. bobpursley

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?
how long= 1+2.79 hours

2. Reiny

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

3. bobpursley

reiny is correct, my rate for AandC has an error.

4. Melvin

noted

## Similar Questions

1. ### college algebra

Find the time for two people working together to complete half a task if it takes them 8 hours and 10 hours to complete the entire task working individually.
2. ### college algebra

Find the time for 2 people working together to complete half of a task if it takes them 8 hours and 10 hours to complete the entire task working individually. Thank you!!!
3. ### arithmetic

How do I get hours to perform task I have a rate of 28 per hour and 6245 transactions how many hours to complete
4. ### math

it takes janet 9 hours to do a task and it take jancie 10 hours to do the same task how long will it take both of them to do the task together
5. ### math

if wayne completed a task in one hour and sarah completed a task in two hours, how long will they take if they work together?
6. ### Math/Management

Ten jobs are to be completed by three workers (Sam, Joy, and Kelly) during the next week. Each person works a 40-hour week and is paid an hourly rate: Sam, Joy, and Kelly earn \$11, \$13, and \$14 per hour, respectively. Union rules require …
7. ### math

If A and B work together,they can finish a task in 2 hours. If they do the task separately, B can finish 3 hours earlier than A can. Find the time required for B to finish the task alone.
8. ### Algebra

Working​ together, Sarah and Jeff can do a task in 6 hours. Jeff uses a motorized cart to do the​ task, whereas Sarah uses a pushcart. If each person does the task without the help of the​ other, it takes Sarah twice as long …
9. ### Math

A man can do a certain task in 21 hours, another man can do the task in 28 hours and a boy can do the task in 48 hours. Find how long it will take to do the task if all three work.
10. ### algebra

A man can do a certain task in 21 hours, another man can do the task in 28 hours and a boy can do the task in 48 hours. Find how long it will take to do the task if all three work.

More Similar Questions