if tony took 24 hours to finish his homework and sally took 30 hours. if they work together how many hours they would take?

Do you mean that each does half of the homework and then they share their answers?

That sounds like cheating to me.

What the heck is your deal Sue. It's a math question, you think the math teacher is going to accept "That sounds like cheating ;(" on a test? Grow up!

To determine how many hours Tony and Sally would take to finish their homework together, we can use the concept of work rates. The work rate is defined as the amount of work completed per unit of time.

Let's find the work rate for Tony and Sally individually:
Tony's work rate = 1 homework / 24 hours = 1/24 homework per hour
Sally's work rate = 1 homework / 30 hours = 1/30 homework per hour

Now, to find how long it would take them to finish together, we can add their work rates:
Combined work rate = Tony's work rate + Sally's work rate
Combined work rate = 1/24 + 1/30 homework per hour

To simplify the calculation, we can find a common denominator for the fractions:
Combined work rate = (30/30)*(1/24) + (24/24)*(1/30) homework per hour
Combined work rate = 30/720 + 24/720 homework per hour
Combined work rate = 54/720 homework per hour

Now, let's find the time it would take for them to finish together using the combined work rate:
Combined time = 1 / Combined work rate
Combined time = 720 / 54 hours

Simplifying the fraction:
Combined time = 40/3 hours

So, Tony and Sally would take approximately 13.33 hours to finish their homework together.