A can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?Options33/841/1042/1140/9
Question
A can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?Options33/841/1042/1140/9
Solution 1
To solve this problem, we first need to find the rate at which A and B can complete the work.
- A can complete the work in 8 days, so A's work rate is 1/8 of the work per day.
- B can complete the work in 10 days, so B's work rate is 1/10 of the work per day.
When A and B work together, their rates of work are added together.
So, the combined work rate of A and B is 1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the work per day.
To find out how long it would take for them to complete the work together, we divide the total work (which is 1) by their combined rate.
So, the time it would take is 1 / (9/40) = 40/9 days.
Therefore, the correct answer is 40/9 days.
Solution 2
To solve this problem, we first need to find the rate at which A and B can complete the work.
- A can complete the work in 8 days, so A's work rate is 1/8 of the work per day.
- B can complete the work in 10 days, so B's work rate is 1/10 of the work per day.
When A and B work together, their rates of work are added. So, the combined work rate of A and B is 1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the work per day.
To find out how many days it would take for both A and B to finish the work together, we divide the total work (which is 1) by their combined work rate (which is 9/40).
So, 1 ÷ (9/40) = 40/9 days.
Therefore, it would take 40/9 days for both A and B to finish the same work together. So, the correct option is 40/9.
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