it takes beth 6 hours to do homework and it takes nina 9 hours. how many hours would it take if they did their homework together?

find the average of hours of homework completion.

(6+9)/2 = 7.5 hours

If they have to do their OWN homework, then the question really makes no sense.

If it is an assignment type homework were both can work on the project, then

beth's rate = 1/6
nina's rate = 1/9
combined rate = 1/6 + 1/9 = 5/18
time at combined rate = 1/(5/18)
= 18/5 or 3.6 hrs

To find out how many hours it would take if Beth and Nina did their homework together, we need to calculate their combined work rate.

The work rate can be thought of as the fraction of the task completed per unit of time. In this case, Beth completes the homework in 6 hours, so her work rate is 1/6 (one task completed in 6 hours). Similarly, Nina completes the homework in 9 hours, so her work rate is 1/9.

To calculate their combined work rate, we add their individual work rates together:

Combined work rate = Beth's work rate + Nina's work rate
= 1/6 + 1/9

To add the fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 6 and 9 is 18. So, we can rewrite the fractions with the common denominator:

Combined work rate = (1/6)*(3/3) + (1/9)*(2/2)
= 3/18 + 2/18
= 5/18

Now, we know that the combined work rate is 5/18. To find out how many hours it would take if they did their homework together, we can use the formula:

Time = 1 / Combined work rate

Time = 1 / (5/18)

To divide by a fraction, we can multiply by its reciprocal:

Time = 1 * (18/5)
= 18/5
= 3.6 hours

Therefore, it would take Beth and Nina approximately 3.6 hours to complete their homework together.