Question

If A can do a job in 8 days and b can do the same job in 12 days, how long would it take them both to complete the job working together?
1. 3
2. 4.8
3. 10
4. 5.8
5. 6

Answer 1

You divide the product of the numbers by their sum.
\[\frac{(8)(12)}{8+12}\]

Answer 2

number 2.

Answer 3

A can do the job in 8 days. So his rate is 1/8 of a job per day. B can do the job in 12 days, so his rate is 1/12 of a job per day. Add the two rates to get the total rate of 1/8+1/12 = 5/24.

Now use the idea that Rate * Time = 1 where 1 represents 1 job completed. So we get

(5/24)*t = 1
t = 24/5
t = 4 4/5
t = 4.8

So it will take 4.8 days for them to work together.