Not sure how to set it up?

Nancy and Ned both work for a botanical garden. The botanical garden is adding a number of floral designs around its grounds. Nancy, who has more experience, can plant the flower and make the design by herself in 3 hours. It takes Ned 5 hours working by himself to make the same design. If Nancy and Ned are assigned to work together, how long will it take them to make the design?

Not sure how to set it up?
Nancy can do a full job in 3 hours, so her rate of work is "1 job per 3 hours". Or since she can to 1/3 of the job in one hour, we could say her rate is 1/3 job per hour. Likewise, Ned's rate is 1/5 job per hour. Let t be the number of hours working at the job. Then after t time, Nacy can do (1/3)t of the job and Ned can do (1/5)t. We want to add these together to add up to 1 (for "1 job", which means the whole project. So our equation is:





(1/3)t + (1/5)t = 1





You can multiply both sides of this by 15 to cancel out the fractions, then solve for t.
Reply:To set this one up, think about how much of the design each person can make in one hour. Since Nancy takes 3 hours, in one hour she will have finished 1/3 of the float. Likewise, Ned will have finished 1/5 of the float in one hour. So both of them working together can finish 1/3+1/5 of the float in one hour. You should be able to figure out the rest from here. =) If you need more help, just let me know.
Reply:There is a simple formula you can use: Together/Separate + Together/Separate = 1.





Let Nancy represent the first T/S and Ned represent the second T/S. We know the Separate times of each are 3 and 5 respectively. We are trying to find the time it Together takes them to do the one job.





Hence, set it up at x/3 + x/5 = 1. Find Least Common Denominator of 15.





Thus, 5x/15 + 3x/15 = 15/15. Since the x's are on top, you can basically ignore the denominator 15s for actually solving the problem.





5x + 3x = 15, means 8x = 15. So, x = 15/8 which is a little less than 2 hours. If you desire it to be in minutes, it is 7 and 1/2 minutes under 2 hours; ie, 1 hour and 52 and 1/2 minutes for them to do together.