SOLUTION: Please show me how to solve this. Thanks. After painting a fence together for t hours, Johnson and Maggie have done fractional parts of the job equal to t/4 and t/5 respectfully

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Please show me how to solve this. Thanks. After painting a fence together for t hours, Johnson and Maggie have done fractional parts of the job equal to t/4 and t/5 respectfully      Log On


   

Question 18304: Please show me how to solve this. Thanks.
After painting a fence together for t hours, Johnson and Maggie have done fractional parts of the job equal to t/4 and t/5 respectfully. How much time T(in hours, minutes and seconds) is required to compeltely paint the fence assuming no breaks.
T = _ hours _ minutes _ seconds
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One approach is to find the hourly rate of Johnson and that of Maggie.
If t = number of hours, then, if t = 1 hour, Johnson can paint 1/4 of the fence in i hour and Maggie can paint 1/5 of the fence in 1 hour.
Together, they can paint (1/4 + 1/5) of the entire fence in 1 hour.
1%2F4+%2B+1%2F5+=+9%2F20
So, in 1 hour, they can paint 9/20 of the entire fence working together.
Therefore, it would take them 20/9 hours to paint the entire fence together.
20/9 hours = 2 2/9 hours.
2/9 hours = 13 1/3 minutes.
1/3 minute = 20 seconds.
20/9 hours = 2 hours 13 minutes 20 seconds.
T = 2 hours 13 minutes 20 seconds.