Algebra 1, Math

Question

When Sean and Allen work together, they can paint a fence in 9 hours. Working alone, Sean can paint the fence in 1/3 of the amount of time that it takes Allen to paint the fence. How many hours would it take Allen to paint the fence alone?

Answer 1

Let t = the number of hours it takes Allen to paint the fence alone

Let (1/3)t = the number of hours it takes Sean to paint the fence alone

 

time together/time alone + time together/time alone = 1

9/t + 9/(1/3)t = 1       Multiply both sides by 3t

27 + 9 = 3t

36 = 3t

12 hours = t

 

Answer 2

a represents the time it would take Sean alone

3a represents the time it would take Allen alon

 

a/9 + 3a/9 = 1

 

Can you solve for a and answer?