Question

A and B can do a piece of eork separately in 8 and 12 hours. If they work alternate hours, A starting, when will the work be finished ​

Answer 1

Answer:

9 and a half hours.

Explanation:

If A takes 8 hours to complete it, they work at a rate of 1/8th of the work per hour. Then, if B takes 12 hours, they take 1/12th of an hour.

Hour 1 (A): 1/8

Hour 2 (B): 1/8 + 1/12= 5/24

Hour 3 (A): 5/24 + 1/8= 8/24

Hour 4 (B): 8/24 + 1/12=10/24

Hour 5 (A): 10/24 + 1/8=13/24

Hour 6 (B): 13/24 + 1/12=15/24

Hour 7 (A): 15/24 + 1/8=18/24

Hour 8 (B): 18/24 + 1/12=20/24

Hour 9 (A): 20/24 + 1/8=23/24

Now, we only need another 1/24th, or half of 1/12th. Therefore, you have the full 9 hours and a half.

Good luck, message me if you want more deets or a maths tutor on Discord (Steven Universe Naomi#6511) :D